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DEPARTMENT OF COMMERCE AND LABOR 



t 




OF THE 



Bureau of Standards 



S. W. STRATTON. Director 



Volume 4 

(Nos. 1. 2. 3. 4) 

1907-8 




WASHINGTON 

GOVERNMENT PRINTING OFRCE 

1906 






./ 



^^-\ 



\jv^. -.j«^\A cv\V^K, 



CONTENTS OF VOLUME 4. 

[Nonrs. — ^The number preceding the title of each article is the Reprint Number in the series of tech- 
nical papers issued by the Bureau.] 



NO. 1. 

[Issued December, 1907.] 

Page. 

70. Clark and Weston Standard Cells F. A. Wolff and C. E. Waters i 

71. The Electrode Equilibrium of the Standard Cell 

F. A, Wolff and C. E. Waters 81 

72. A Comparative Study op Plain and Frosted Lamps 

£. P. Hyde and F, E. Cody 91 

73. The Variation op Resistances with Atmospheric Humtoity 

E. B. Rosa and H. D. Bahcock 121 

74. On the Self-Inductance of a Toroidal Coil op Rectangular* Sec- 

— - TION Edward B. Rosa 141 

75. On the Selp-Inductancb op Cirql^.. Edward B.Rosa and Louis Cohen 149 

76. The Influence op Frequency on the Resistance and Inductance 

OF SolEnoidal Coils Louis Cohen 161 

NO. 2. 

[Issued January. 1908.] 

77. The Atomic Weight op Hydrogen W. A. Noyes 179 

78. On the Best Method op Demagnetizing Iron in Magnetic Testing 

C. W, Burrows 205 

79. A Deflection Potentiometer for Voltmeter Testing.. H. B. Brooks 275 

80. The Self and Mutual-Inductance of Linear Conductors 

Edward B. Rosa 301 

NO. 3. 

[Issued January, X908.] 

81. The Atomic Weight of Chlorine W. A. Noyes and H. C. P. Weber 345 

82. The Preparation of Chloroplatinic Acid by Electrolysis op Plati- 

num Black H. C. P. Weber 365 

83. The Self-Inductance of a Coil op any Length and any Number of 

Layers op Wire Edward B. Rosa 369 

84 The Self-Inductance of a Solenoid of any Number of Layers 

Louis Cohen 383 

85. Instruments and Methods Used in Radiometry W, W. Cobleniz 391 

86. A Quartz Compensating Polariscope with Adjustable Sensibility. . 

Frederick Bates 461 



I<S79J3 



IV Contents of Volume 4. 

NO. 4. 

[Issued May, X908.] 

Page. 

87. Apparatus for Dgtbrmination op the Form op a Wave of Magnetic 

Flux M.G. Lloyd and J. V. S. Fisher 467 

88. Effect op Wave Form Upon the Iron Losses in Transformers 

Morton G. Lloyd 477 

89. The Luminous Properties of Electrically Conducting Helium Gas. . 

P. G. Nutting 5 1 1 

90. Function of a Periodic Variable Given by the Steady Reading of 

Ai* Instrument; with a Note on the Use op the Capillary Elec- 
trometer WITH Alternating Voltages Morton G. Lloyd 525 

91. Selective Radiation from the Nernst Glower W. H'. Coblcniz 533 

92. The Testing of Glass Volumetric Apparatus 

N. S. Osborne and B. H. Vcazey 533 




CLARK AND WESTON STANDARD CELLS. 



By F. A. Wolff and C E. Waters. 



mXRODUCTION. 

The important r61e now played by the standard cell in both tech- 
nical and scientific work, and the possibility of its adoption as a 
primary standard of electromotive force, have led in recent years to 
a considerable number of investigations concerning its reproduci- 
bility and constancy. The character of these investigations and the 
results obtained will, however, be better understood after a brief 
review of the previous work on the subject. 

The need of a definite and universal system of electrical units was 
early recognized. Owing to its preponderating importance in the 
earlier applications of electricity, the unit of resistance naturally 
received first attention. The committee on electrical standards 
appointed by the British Association in 1861 recommended the 
adoption of the C. G. S. electromagnetic system together with a 
practical system defined as decimal multiples and submultiples of 
the C. G. S. units. In addition, its labors led to the construction of 
concrete standards of resistance in the form of coils of platinum- 
silver of special design adjusted to represent lo* C. G. S. units as 
determined by a series of absolute measurements. 

The definition of unit current and electromotive force in terms of 
the C. G. S. units long met every requirement, particularly as currents 
were generally measured by the aid of the tangent galvanometer, 
while electromotive forces were generally measured in terms of the 
electromotive force of the Daniell cell. 

In 1872 Latimer Clark called to the attention of the British Asso- 
ciation committee the superiority of the cell which now bears his 



2 Bulletin of the Bureau of Standards, [roi. 4, No. i. 

name, recommending it as a suitable standard of electromotive force. 
In its original form * it consisted of a mercury electrode covered with 
a paste made of mercurous sulphate, zinc sulphate crystals and solu- 
tion, while a rod of zinc in a saturated zinc sulphate solution above 
the mercury and paste and in contact with an excess of zinc sul- 
phate crystals formed the second electrode. It will thus be seen that 
Clark fully appreciated the importance of reversibility, a fundamen- 
tal condition to be satisfied by the standard cell. Clark also fore- 
saw nearly all of the modem applications of the standard cell, as for 
example in the calibration of the ballistic galvanometer, in main- 
taining a current at a constant value, in the measurement of cur- 
rents and electromotive forces, etc. No action was, however, taken 
on the suggestion by the committee. 

The discovery of considerable error in the British Association ohm 
determination, the rapid development of electrotechnics, and the 
resulting demand for increased accuracy induced the French Gov- 
ernment to issue a call for an international electrical congress to 
meet in Paris in 1881. This was followed by an international 
commission, recommended by the congress, which met in 1882 and 
1884, and which defined the ohm in terms of the Siemens mercury 
unit, the ampere as one-tenth of a C. G. S. unit of current and the 
volt in terms of the ohm and ampere. 

While the demands for accuracy of reproduction were fully met 
by the mercury ohm, the definitions of the ampere and the volt were 
found to be far from satisfactory. During the next few years atten- 
tion was therefore directed to the investigation of the silver cou- 
lometer and the Clark cell. The former was studied by Mascart (•), 
Rayleigh and Sidgwick ('), Kohlrausch (*), and others. 

Rayleigh's ^ investigations on the Clark cell showed that the main 
variations could be traced to impurities in the materials employed 
and to a faulty construction, the zinc not being completely covered 
with zinc sulphate crystals, thus retarding the attainment of satura- 
tion equilibrium for the temperature of observation. To remedy 

*Phil. Trans. Roy. Soc., 164, p. i; 1874. 

2 Jour, de Phys. (2), 1, p. 109; 1882. Jour, de Phys. (2), 8, p. 283; 1884. 

3 Phil. Trans. Roy. Soc, 175, p. 411; 1884. 

* Wied. Ann., 27, p. i; 1886. 

«Phil. Trans. Roy. Soc., 176, p. 781; 1885. 



i 



DEPARTMENT OF COSTRrERCE AlO) LABOR 



Bulletin 



No. 1 



Bureau of Standards 



-TRATTOr 



l'£' 



CONTENTS 



CUiLC l»3 W»1bQ Sttiitlftr-! tt^' 



(HNERJimi 



mfui-s.^ Clark and Weston Standard Cells, 3 

the latter defect Rayleigh proposed the H cell in which the zinc rod 
of the older type was replaced b)' zinc amalgam. Another cause of 
wide variations in Clark cells was found by Rayleigh to be a trans- 
formation of zinc sulphate, stable at ordinary temperatures as hepta- 
hydrate, into the hexahydrate at temperatures above 40? Rayleigh 
showed that the inverted form persisted in a metastable condition 
for a long period after cooling, thus explaining the abnormal values 
which were frequently observed, and which were probably the rule 
when the older specifications which prescribed heating the constitu- 
ents to boiling were followed. 

I^ittle further work was done on the Clark cell until shortly before 
the Chicago International Electrical Congress. In England the 
subject was taken up in 1891 by Glazebrook and Skinner,* in con- 
nection with a committee appointed by the Board of Trade on 
Standards of Electrical Measurement. They studied the reprodu- 
cibility of Clark cells constructed by themselves and others, deter- 
mined the limits of error to be expected, and redetermined the elec- 
tromotive force in terms of the electrochemical equivalent of silver. 
The cells set up by them were all of the Board of Trade type and 
an accuracy of only o.oi per cent was sought. 

The subject was taken up about the same time at the Reichsan- 
stalt by Kahle,^ who used specially purified materials and made a 
carefnl study of the influence of added impurities. Practically all 
of his work was done with cells of the H type, with which trustworthy 
measurements could be made to a few hundred thousandths of a volt. 
Unfortunately, he employed only one sample of mercurous sulphate, 
the constituent which has since been found to be the main source of 
variation. Later he also made a redetermination of the tempera- 
ture coefficient and the absolute value.' 

From the results obtained it was found that there was little choice 
between the standard cell and coulometer from the standpoint of 
accuracy ; indeed, both the coulometer and the cell were adopted in 
the definitions of the ampere and volt by the Chicago congress. 

•Phil. Trans. Roy. Soc., 188, p. 567; 1892. 
iTa, fiir Instrk., 12, p. 117; 1892. 
Zs. fur Instrk., 18, p. 293; 1893. 
Wied. Ann., 51, p. 174; 1894. 
l«Zs. fiir Instrk., 18, p. 230; 1898. 
Wied. Ann., 67, p. i; 1899. 



4 Bulletin of the Bureau of Standards, [roi. 4. no. i. 

Subsequent to the Chicago congress the temperature coefficient 
of the Clark cell was redetermined by Jaeger and Kahle and also by 
Callendar and Barnes, with close agreement between the two. 

Further studies on the hysteresis,* polarization," and the inversion 
of zinc sulphate" were also made by various investigators. 

In 1892 Edward Weston" described a cell in which the zinc and 
zinc sulphate of the Clark cell are replaced by cadmium and cad- 
mium sulphate, respectively. It was discovered by Weston that a 
cadmium cell set up with a cadmium sulphate solution saturated at 
4° had a negligible temperature coefficient. A portable type was 
also designed and has since been on the market. 

The elaborate studies of the saturated type made at the Reichsan- 
stalt by Jaeger and Wachsmuth," Jaeger," Jaeger and Kahle," and 
Jaeger and Lindeck," indicated that the Weston cell possessed all 
the merits of the Clark cell, besides having a much smaller tempera- 
ture coefficient, showing no tendency to crack at the amalgam limb, 
so frequently observed with Clark cells, and not forming gas at the 
amalgam electrode. 

In the specifications first proposed by Jaeger for the cadmium cell 
a 1 : 6 cadmium amalgam was recommended, the employment of 
which led to considerable mistrust, as irregularities of behavior were 

• Ayrton and Cooper: Proc. Roy. Soc., 69, p. 368; 1896. 

Spiers, Twyman and Waters: Phil. Mag. (5), 45, p. 285; 1896. 

Callendar and Barnes: Proc. Roy. Soc, 62, p. 117; 1897. 
loSkinner: Phil. Mag. (5), 88, p. 271; 1894. 

Wulf : Wien. Sitz-Ber. II a, July, 1897. 

Jaeger: Ann. d. Phys. (4), 14, p. 726; 1904. 
"Jaeger: Wied. Ann., 63, p. 354; 1897. 

Callendar and Barnes: Proc. Roy. Soc, 62, p. 117; 1897. 

Cohen: Zs. f. phys. Chem., 26, p. 300; 1898. 

Cohen: Zs. f. phys. Chem., 81, p. 164; 1899. 

Cohen: Zs. f. phys. Chem., 84, p. 62; 612; 1900. 

Barnes: Jour, of Phys. Chem., 4, p. i; 1900. 
"Electrician, Lond., 80, p. 741; 1893. 
"Electrotech. Zs., 16, p. 507; 1894. 
"Eledrotech. Zs., 18, p. 647; 1897. 
»Zs. fiirlnstrk., 18, p. 161; 1898. 

Wied. Ann., 66, p. 926; 1898. 
"Zs. fiir Instrk., 21, 33 ; 1901. 

Ann. d. Phys. (4), 6, p. i ; 1901. 



H^urs^ Clark and Weston Standard Cells. 5 

observed by Callendar and Barnes and confirmed by others " at tem- 
peratures below 15? These were first attributed to an inversion of 
the cadmium sulphate similar to that of zinc sulphate referred to 
above, but later investigations " showed that they were undoubtedly 
due to the cadmium amalgam and were entirely eliminated by the 
employment of 12-13 per cent amalgams. 

Further work by Bijl " and Puschin ^ has shown that cadmium 
amalgams consist within certain temperature limits of a liquid phase 
and a solid phase, the composition of the latter depending on the 
temperature, and that the mixed crystal is therefore an isomorphous 
mixture of cadmium and mercury. With both phases coexistent, 
the electromotive force toward cadmium sulphate at a given tempera- 
ture is independent of the relative amounts of the metals present, as 
found by Jaeger,** while in the absence of the liquid phase irregu- 
larities in behavior are found. The composition of the amalgam 
to be employed in the standard cell must therefore be such that both 
phases will be present within the usual temperature range 0° to 40°, 
a condition satisfied by the 12.5 per cent amalgam, now in general 
use. 

Previously unsuspected irregularities due to the mercurous sul- 
phate were observ^ed at the Reichsanstalt toward the end of 1900,** 
when a sample of mercurous sulphate, obtained from a different 
source, was employed. Even after the cells had reached constant 
values they were still several tenths of a millivolt higher than the 
older cells all made from another sample of mercurous sulphate. 

In 1904 an investigation of the subject was begun in temporary 
quarters at the Bureau of Standards by one of the authors and Dr. 



" Callendar and Barnes: Electrician, 89, p. 638; 1897. 

Cohen: Wied. Ann., 60, p. 344; 1898. 

Cohen: Zs. f. phys. Chem., 84, p. 621; 1900. 
"Jaeger: Wied. Ann., 65, p. 106; 1898. 

Zs. fiir Instrk., 20, p. 317; 1900. 

Ann. d. Phys. (4), 8, p. 366; 1900. 

Ann. d. Phys. (4), 4, p. 123; 1901. 

von Steinwehr: Ann. d. Phys. (4), 9, p. 1046; 1902. 
"Zs. fiir phys. Chem., 41, p. 641; 1902. 
*Jr. Russ. phys. Chem. Soc, 84, p. 856; 1902. 

Zs. fiir anorg. Chem., 86, p. 201; 1903. 
"Wied. Ann., 65, p. 106; 1898. 
"Jaeger and Lindeck: Zs. fiir Instrk., 21, p. 73; 1901. 



6 Bulletin of the Bureau of Standards, \vol 4, no. i. 

H. N. Stokes. Some preliminary work was done on the purification 
of materials, but efforts were mainly directed to the preparation of 
mercurous sulphate of uniform electromotive properties, an electro- 
lytic method being devised. This method was described by one of 
the authors ** at the Washington meeting of the American Electro- 
chemical Society, April 7, 1904, at which a paper by Carhart and 
Hulett," giving essentially the same method, was also read. A num- 
ber of cells, set up with samples of mercurous sulphate prepared by 
this method, showed excellent agreement among themselves." The 
work at the Bureau was interrupted by the establishment of the 
branch laboratory at St. Louis and by the extra work incident to 
moving into the new laboratories at Washington. 

Considerable further work has been done by Hulett" on the repro- 
ducibility of the Weston cell, in connection with which a study was 
made of the influence of hydrolysis of the mercurous sulphate. It 
was shown by Gouy*^ that pure mercurous sulphate is hydrolyzed 
by water with the formation of a yellowish, difficultly soluble, basic 
product, which he stated is easily transformed into neutral mer- 
curous sulphate by o.i normal sulphuric acid. He also stated 
that mercurous sulphate is not hydrolyzed by saturated solutions 
of zinc or cadmium sulphate. 

Hulett, on the other hand, by rotating a sample of mercurous sul- 
phate with mercury and successive portions of water at constant 
temperature, found that the electrical conductivity of the solution 
remained constant until all the mercurous sulphate was hydrolyzed, 
after which a different, fixed conductivity was observed. He found 
that the completely hydrolyzed product was gray, and not yellow. 
He also concluded that a soluble acid sulphate and a slightly solu- 
ble basic sulphate are formed, and that the hydrolyzed salt does not 
dissolve as such, but is further decomposed by water. He also 
determined the solubility curves of mercurous sulphate, in the pres- 

** Wolff: Trans., Am. Electrochem. Soc., 5, p. 49; 1904. 
»*Ibid., 5, p. 59; 1904. 

"'These were ruined by exposure to light after removal to the new laboratory and 
during Doctor Wolff's absence on duty at the St. Louis Exposition. 
••Zs. fiir phys. Chem., 49, p. 483; 1904. 

Phys. Rev., 22, p. 321; 1906. 

Phys. Rev., 28, p. 166; 1906. 
•'Compt. rend., 180, p. 1399; 1900. 



\ya^s.^ Clark and Weston Standard Cells. 7 

ence of mercur}-, in sulphuric acid of vaiying concentrations, and 
found a maximum solubility at V=i (F denoting the number of 
liters containing- one mole sulphuric acid) and a break in the curve 
at F= 4, from which he concluded that hydrolysis apparently begins 
at this dilution. 

Hulett set up a considerable number of cells with samples of 
mercurous sulphate prepared by the electrolytic method, varying the 
current density and strength of acid between wide limits, and also 
with samples prepared by chemical methods. Where the concen- 
tration of the acid was less than molecular, the electrolytic samples, 
which were white even with the greatest current density, gave 
higher results than the gray samples obtained when stronger acid 
was used, and which showed excellent agreement among themselves. 
Less satisfactory' results were obtained with samples prepared by 
chemical methods. 

He also found that cells in which the depolarizer was a mixture 
of neutral and completely hydrolyzed mercurous sulphate gave 
values irregularly increasing with the percentage of basic sulphate 
employed. For other cells the mixture was prepared by rotating 
mercurous sulphate with definite amounts of water, thus giving a 
definite percentage of basic salt These cells had, however, consid- 
erably higher values, for the same percentage of basic sulphate, 
than those mentioned above. The above results, unexpected in the 
light of the phase rule, are attributed to the possible formation of 
new phases. According to the above there should be a condition 
of unstable equilibrium to which Hulett attributes the slow decrease 
of e. m. f. observed by him in older cells. This was further tested 
by single electrodes charged with a mixture of mercury, mercurous 
sulphate and cadmium sulphate, the materials being rotated for a 
number of days in a thermostat. When measured against an amal- 
gam electrode abnormally high values were observed, which 
decreased on stopping the rotation. These cells were not kept 
under observation long enough to determine whether normal values 
would be reached. It is to be noted that this effect will not account 
for the decrease in the e. m. f., observed by Hulett in the case of old 
cells, except on the assumption that further reaction takes place 
between the products of hydrolysis and the ingredients of the cell. 
This will be discussed more fully in a later paper. 



8 Bulletin of the Bureau of Standards, \voi. 4, no. i. 

At the Reichsanstalt a special study has been made of the influ- 
ence of size of grain on the electromotive properties of mercurous 
sulphate. According to v. Steinwehr**, this is mainly responsible 
for variations noted in the case of commercial samples, fine-grained 
samples giving, in accordance with theory, much higher values 
than coarse-grained ones. On grinding the latter he found a con- 
siderable increase in the e. m. f. and a very slow recovery. 

Work on the standard cell has been in progress for several years 
at the English National Physical Laboratory," but no detailed 
report of the results has been published. According to preliminary 
reports considerable progress has been made. Samples of mercu- 
rous sulphate prepared by three chemical methods agree in e. m. f. 
with samples prepared by the electrolytic method. 

In October, 1905, the work was resumed by the present authors 
with the object of investigating the purification and preparation of 
materials for Clark and Weston cells, the influence of impurities, 
and any other sources of variation, such as size of grain, etc., influen- 
cing the electromotive force. 
i A systematic study of reproducibility can of course be made only 

by comparing the various materials in actual cells in which only 
one ingredient is varied at a time. It was therefore necessary to 
set up a large number, and in order to employ identical materials a 
considerable supply had to be accumulated, which, in the case of 
cadmium sulphate, required a long time, as our object was, at first, 
to employ only clear crystals, though it has since been found that 
cloudy crystals from a purified solution give the same electromotive 
force. 

The details and results of the work done at the Bureau of Stand- 
ards, a brief account of which was given at the New York meeting 
of the American Physical Society, December, 1906,'^^ are submitted 
below under the following heads: 

'^Zs. fur Instrk., 26, p. 205; 1905. 

Zs. fiir Elektrochem., 12, p. 578; 1906. 
"Smith: B. A. Reports 1904, 1905, and 1906. 

Electrician (Lond.), 5o, p. 857; 1905. 
»>Wolff and Waters: El. World, 49, p. 100; 1907. 
Phys. Rev., 24, p. 252; 1907. 
Electrician (Lond.), 58, p. 692; 1907. 



^urs^ C7ar^ and Weston Standard Cells. 9 

Preparation and purification of materials. 

The cells. 

The comparing baths. 

The electrical measurements. 

Tabulation of results. 

Discussion of results. 

General conclusions. 

PREPARATION AND PURIFICATION OF THE MATERIALS. 

Mercury, — All the mercury used in this investigation was puri- 
fied by distilling it at least twice in a current of air under greatly 
reduced pressure, according to Hulett and Minchin.'* 

The essential feature of this method is the oxidation of any metals 
that may distil with the mercury by means of a slow current of air, 
admitted through a tube drawn out at one end to a very fine capil- 
lary extending almost to the bottom of the distilling bulb. This 
tube passes through a tightly fitting cork in the neck of the bulb, 
and the flow of air is regulated by means of a pinchcock and a short 
piece of rubber tubing, the free end of which is plugged with cotton 
wool to filter out dust. To prevent charring the cork a bulb with 
the side tube as low as possible on the neck should be selected. 

An ordinary distilling bulb, of about 500 cc capacity, is sealed to 
one end of a slightly inclined, wide tube, 2 cm in diameter and 50 
cm long, which serves as the condenser. At the lower end of the 
condenser is sealed a vertical tube of 3 to 4 mm bore and 80 to 90 cm 
in length, and bent into S form at the lower end, which thus serves 
as a trap for the mercury, which runs out, as rapidly as it distils, 
into a beaker or small dish. A side tube must be sealed to the 
upper, slightly widened part of the vertical tube for making con- 
nection with an aspirator. On commencing the distillation the 
vertical tube is filled by placing under the lower end a small beaker 
of mercury and then starting the aspirator. Of course somewhat 
more of the first part of the distillate than is needed to fill the 
vertical tube must be rejected. 

As an additional precaution against mercury being carried over 
by bumping, a Claisen distilling bulb, with two necks, instead of 

« Phys. Rev., 21, p. 388; 1905. 



lo Bulletin of the Bureau of Standards, \voi. 4, No. /. 

one of the ordinary form, was employed by the authors, a ther- 
mometer being inserted in the second neck. The flasjc was heated 
in a hemispherical iron dish, the bulb being surrounded by a loose 
cylindrical sheath of asbestos paper and a cover of asbestos board 
through which the necks of the flask passed. By using iron turn- 
ings in the bath, instead of sand, which might scratch the bulb, and 
allowing at least an hour for cooling before refilling with mercur>', 
it was possible to distil a large quantity of mercury without any 
apparent damage to the bulb. 

From time to time the still was cut apart, cleaned with nitric 
acid, washed and dried. Usually about four-fifths of the mercury 
was distilled over, and when it was not very impure, the residue 
was simply sucked from the flask by means of a pipette. 

The surface of the distilled mercury was slightly coated with 
oxides of the metals originally contained in it. These were removed 
by passing it through a pinhole in a filter paper. 

In most of the work commercial mercury was distilled at least 
twice by this method. Some which had been used in the laboratory 
and was badly contaminated was, however, first subjected to a pre- 
liminary purification by electrolysis. This was found to be simpler 
and more efficient than the usual treatment with dilute nitric acid 
or mercurous nitrate, the action of which is necessarily superficial 
and therefore slow. 

By making the mercury the anode, a piece of platinum foil the 
cathode, and using 2 per cent nitric acid as the electrolyte, the more 
positive metals go almost completely into solution by electrolysis, 
leaving in the mercury the less positive metals which exert only a 
minor influence on the e. m. f. and which may with the others be 
afterwards removed by distillation as described above. 

With a current density of about 0.5 ampere per square decimeter, 
the electrolysis was continued, constantly stirring the mercury, for 
some hours after it no longer tailed, the time required depending on 
the amount and the original condition of the sample. The mercury 
deposited on the cathode, possibly containing some of the electro- 
positive impurities, was prevented from dropping back into the 
anode mercury by suspending under the cathode a small beaker 
hung from the side of the battery jar by means of a support made 
of glass rod. The combination anode and stirrer described below 



H^^s2 Clark and Weston Standard Cells. ii 

was used. The depth of the mercury was great enough to com- 
pletely cover the blades of the stirrer when rotating, and the volume 
of dilute acid employed was about four times that of the mercury. 

Twenty kilos of mercury, very impure from use in the laboratory, 
were subjected to this purification using a current of i ampere for 
seventeen hours, and then distilled in three successive portions, 
leaving the residue in the bulb each time. Then 7 kilos more of 
mercury, also purified electrolytically, were introduced and distilled. 
The final residue, amounting to about i kilo, was analyzed. Traces 
of zinc, iron, and copper, and a small amount of lead were found. 
In the mercury before distillation no lead was found and only a 
doubtful reaction for zinc was obtained, while copper and iron were 
detected. 

Zinc, — To remove small quantities of cadmium, lead, iron, and 
arsenic ordinarily contained in the commercial chemically pure metal, 
a considerable quantity of Kahlbaum's best zinc was repeatedly dis- 
tilled under diminished pressure according to the method of Morse 
and Burton.'* A large tube of Jena combustion glass was closed at 
one end, the zinc introduced, and the tube drawn out at equal inter- 
vals, thus forming three reservoirs. The narrow portions were 
arched somewhat to prevent the melted metal from flowing from 
one section to another. The tube was placed in a combustion fur- 
nace, connected by means of a rubber stopper and heavy tubing to 
a Geryk pump and exhausted, the pump being kept running, not 
only during the distillation but afterwards, until the tube cooled. 
The latter was first heated at the closed end and by smaller flames 
under the second section, care being taken not to allow the tube to 
soften and collapse. The flames were regulated so that nearly all 
the metal condensed in the second section. When about three- 
fourths of the zinc had distilled off, the second section was more 
strongly heated and the zinc distilled into the third section, thus 
effecting a double distillation in practically one operation. The 
flames under the closed end of the tube were turned low, but not 
extinguished, so that the metal would not distil back again into the 
first section. The flames were then extinguished, but air was not 
admitted until the tube was cold. The distilled metal adhered 

»Am. Chem. Jour., 10, p. 311; 1888. 



12 Bulletin of the Bureau of Standards, ivoi. 4, No. i. 

strongly to the glass, which was removed by hammering with a 
porcelain pestle. 

In some of the work, zinc, which had been distilled in this 
manner three times, was used, but in most of the cells Kahlbaum's 
best zinc was employed without further treatment, as it was found 
to give identical results. 

Cadmium. — Kahlbaum's best cadmium, prepared electrolytically, 
was distilled five times in the same manner as the zinc.'' In most 
of the cells, however, the metal was used without further treatment. 
Although considerable platinum was found in the residues and a 
trace of arsenic in the portions of the distillate which condensed 
beyond the third section of the tube, the original metal was found 
to give the same results. 

Amalgams, — Zinc amalgam^ containing 10 per cent by weight of 
zinc, was prepared by dissolving a weighed amount of pure zinc in 
nine times its weight of pure mercury. The latter was heated 
gently in a porcelain dish on a sand bath. The zinc, previously 
treated with very dilute sulphuric acid to remove the film of oxide, 
then washed with water and dried, was placed upon the hot mercury 
and frequently stirred to hasten solution, the heat being increased 
whenever the amalgam showed a tendency to solidify. 

Cadmium amalgam^ containing 12.5 per cent by weight of cad- 
mium, was prepared in the same manner. On account of its relatively 
low melting point it was, however, prepared on the steam bath. 

Oxidation of the amalgams, — On exposure to the air the surfaces 
of the amalgams are slowly tarnished by oxidation ; but as consider- 
able changes in composition have no appreciable influence on the 
electromotive force, this is of no practical importance. The oxida- 
tion is lessened by keeping the amalgam under a solution of zinc or 
cadmium sulphate ; but in the course of time a deposit of basic salt 
is formed. Apart from the fact that the use of these solutions does 
not completely prevent oxidation is the further objection that the 
pipette used in introducing the amalgam into the cells may become 
coated with basic sulphate. In addition, the zinc amalgam must 
be heated so high that there is violent bumping. Accordingly 
this method of removing the oxide was abandoned, and the melted 

"Morse and Jones: Am. Chem. Jour., 14, p. 261; 1892. 



^Ta^s^ Clark and Weston Standard Cells, 13 

amalgam was simply strained, when necessary, through a test tube 
drawn out at the bottom to a small opening and heated gently from 
time to time to keep the amalgam melted. 

Zinc sulphate, — The salt is apt to contain sulphates of cadmium, 
iron, lead, etc., and free sulphuric acid. The last of these has the 
greatest effect upon the e. m. f., and promotes the formation of gas in 
the amalgam limb. Although the effect of such small quantities 
of the other impurities as are apt to be contained in the chemically 
pure salt is practically negligible, the following methods of puri- 
fication, both giving the same results with zinc sulphate from 
Kahlbaum and from the J. T. Baker Company, were used: 

The chemically pure salt, as purchased, was dissolved in hot water, 
an excess of pure zinc oxide and sufficient pure hydrogen peroxide to 
effect the oxidation of any ferrous iron added and the solution kept 
at nearly the boiling point for several hours to throw down iron as 
completely as possible. It was then filtered, acidified slightly, and 
evaporated until the zinc sulphate began to crystallize out, then 
cooled with ice (5° or lower), stirring frequently meanwhile so as to 
obtain small crystals. These were filtered off, using a platinum 
cone, washed once or twice with very little ice-cold water, redis- 
solved in a little hot water, and recrystallized as before. Further 
crops of crystals were obtained from the first and second mother- 
liquors, those from the first being recrystallized once, those from the 
second mother-liquor twice. The three lots of crystals were then 
combined and dissolved in sufficient warm water to form a saturated 
solution. The temperature was not allowed to exceed 35° to avoid 
the formation of the hexahydrate, which is stable above 39? The 
solution was filtered, and with continuous stirring, cooled by sur- 
rounding the beaker with ice. The crystals were filtered off, using a 
platinum cone, and washed two or three times with a little ice-cold 
water. The air-dried crystals were preserved in a well stoppered 
bottle. 

The zinc oxide employed was prepared by adding ammonia to a 
solution of zinc sulphate until the precipitate dissolved. It was 
then filtered into a large volume of water, allowed to settle, the 
supernatant liquid decanted, and the precipitate thoroughly washed 
on a Biichner funnel (using a hardened filter paper), removed from 
8919—07 2 



14 Bulletin of the Bureau of Standards, \.voi. 4, No. /, 

the filter paper and ignited in a platinum crucible inclosed in one 
of porcelain to prevent access of reducing gases. 

The zinc sulphate was also purified by electrolysis." After 
removal of iron, as described above, a weak current (about o.i 
ampere per square decimeter) was passed through a nearly saturated 
solution containing suspended zinc oxide to keep it slightly basic. 
Platinum electrodes were used and the solution stirred continuously. 
The electrolysis was continued for several days until a clean anode 
no longer became coated with lead peroxide. The solution was 
sufficiently pure, though it still contained traces of other metals. 
It was filtered, acidified slightly, and the salt twice crystallized 
by evaporating to a small volume. The last crop of crystals was 
dissolved in a small quantity of water at room temperature and the 
solution allowed to evaporate spontaneously. Large, perfect crystals 
were obtained. 

Cadmium sulphate. — The commercial chemically pure salt may 
contain zinc, lead, ferrous and ferric iron, and occasionally nickel. 
Several lots of the salt were purified by dissolving in an excess of 
water at about 70°, filtering when necessary, adding an excess of 
basic cadmium sulphate and a few cubic centimeters of hydrogen 
peroxide to oxidize any ferrous iron present and heating for some 
hours. The solution was then filtered, acidified slightly, and evap- 
orated nearly at its boiling point in a large porcelain dish resting 
on a pipestem triangle on a hot plate or supported some distance 
above the flame of a gas stove. Even then the flakes of the lower 
hydrate of cadmium sulphate which were formed collected on the 
bottom and caused violent bumping unless they were frequently 
removed. The crystals were allowed to drain in a funnel with a 
platinum cone. When the solution had been evaporated to a small 
volume it was poured, while still hot, through the funnel, the crys- 
talline flakes packed down with a pestle, allowed to cool, and washed 
twice with a little cold water, using suction. They were then 
redissolved and the solution evaporated down to a small volume, as 
before. After this operation the crystals were dissolved in a slight 
excess of water at room temperature. The solution was filtered 
when necessary, and then set aside in shallow layers (2 to 3 cm) in 

"Mylius and Fromm: Zs. f. anorg. Chem., 9, p. 144 ; 1895. 



^aurs^ Clark and Weston Standard Cells, 15 

crj^stallizing dishes covered with filter paper. The solution should 
not be saturated when placed in the dishes, especially if it be a 
mother liquor from which a crop of crystals has been removed, for 
the salt is almost certain to come down in a few hours as a crust 
over the bottom instead of isolated crystals. At least three-fourths 
of the crystals were cloudy, but these were found to give the same 
results in the cells as the perfectly clear ones. By varying the rate 
of evaporation and by using acid, neutral and basic solutions, it was 
attempted to obtain a larger proportion of clear crystals, but with- 
out success. The latter, especially, adhered so firmly to the bottom 
of the dish that they were apt to be broken in removal. This was 
obviated by decanting the mother Jiquor and pouring a little pure 
water over the crystals. In a few moments they became loose, 
without going into solution to any great extent, and were easily 
removed with a spatula. They were washed two or three times 
with water and preserved air-dried in bottles. 

Zinc and cadmium sulphate solutions, — The saturated zinc or 
cadmium sulphate solutions required for making up the paste and 
for filling the cells were prepared by agitating an excess of purified 
salt with distilled water. In the case of zinc sulphate shaking with 
water heated to not more than 35° for at least a half hour was sufii- 
cient, while for cadmium sulphate mechanical stirring for three or 
four hours was required on account of the slowness with which it 
dissolved. 

Mercurous sulphate, — The chemically pure mercurous sulphate 
at present obtainable on the market may contain as impurities basic 
mercurous sulphate, basic mercuric sulphate, traces of nitrate, etc., 
according to the method of preparation. In addition the size of grain 
of the commercial samples, usually prepared by rapid precipitation, 
may also have an influence on its electromotive properties. Such 
materials can not, therefore, be directly employed if the highest 
accuracy of reproduction is sought. A considerable number of 
samples of mercurous sulphate was prepared by the following 
methods: 

{a) By electrolysis, old apparatus. 

{b) By electrolysis, new apparatus. 

{c) By the action of fuming sulphuric acid on mercury. 

{d) By the reaction between sulphuric acid and mercurous nitrate. 



i6 



Bulletin of the Bureau of Standards. \voi. 4. No. r. 



{e) By the action of a dilute solution of nitric acid in sulphuric 
acid on mercury. 

(/*) By the reduction of mercuric sulphate by mercury. 

{g) By the reduction of mercuric sulphate by sulphurous acid. 

(Ji) By the recrystallization of commercial mercurous sulphate 
from sulphuric acid. 

(/, k^ /, m^ n) By digestion of commercial mercurous sulphate 
with sulphuric acid. 

All the samples were prepared in subdued light and preserved in 
the dark, to protect them from the action of light. Even diffused 
daylight soon darkens the salt. 




MERCURY 

Rg. 1. — Apparatus for Electrolytic Preparation of Mercurous Su^hate (1904), 

{a) By electrolysis^ old apparatus, — In 1904 an electrolytic method 
of preparation was developed by one of the authors,'' and also inde- 
pendently by Carhart and Hulett,'* the mercurous sulphate being 
formed by the passage of a current at the surface of a mercury anode 
in sulphuric acid. Preliminary experiments, based on the reversi- 
bility of the Clark and Weston standard cells, as shown by the slight 
polarization with weak inverse currents, were made with cadmium 
sulphate solutions. Without stirring a crust of yellow basic mercu- 

•* Wolff: Trans. Amer. Electrochem. Soc, 5, p. 49; 1904. 
"Ibid., 6, p. 59; 1904. 



Waters.} 



Clark and Weston Standard Cells. 



17 



rous and mercuric sulphate was formed and the solution gave a very 
strong mercuric reaction, while with an acidified solution a beautiful 
crystalline product was obtained. 

The anode mercury was contained in a shallow plate, A (fig. i), 
resting on the bottom of a crystallizing dish, B^ of slightly greater 
diameter, placed inside of a second larger crystallizing dish, C, which 
contained the cathode mercury. Both dishes were filled with dilute 
sulphuric acid, covering the inner dish to a depth of several centi- 
meters. Electrical connections were made in the usual manner by 
means of glass tubes with platinum terminals fused into the lower 
ends and filled with mercury. To prevent the possible formation 
of basic compounds and mercuric sulphate, the solution near the 
surface of the anode was stirred continuously. In this way, and with 
a current density not greater than 0.25 ampere per square decimeter, 
the surface of the anode was kept in motion and the mercurous 
sulphate was swept over the edges of the plate as rapidly as it was 











TABLE I. 








Electrolytic Method, Old Apparatus. 


Sample 


Made 


Cone, of 
HSSO4 


Remarks 


*i 


Jan., 


'04 


5% 


-f5% CdSO, 


a.^ 


Mar., 


'04 


2.5% 




*5 


Apr., 
Apr., 


'04 
'04 


5f. 
5,^ 


Slightly brownish on exposed surfaces Mar., '06 


At 


May, 


'04 


1:6 




a^ 


May, 


'04 


1:6 


a^ digested with 25^ H^SO^ 


*s 


May, 


'04 


1:6 




a^ 


May, 


'04 


1:6 


From top of cover dish 


•9 


June, 


'04 


1:6 




aio 


Sept., 


'05 


1:6 


From inside dish 


a'lo 


Sept., 


'05 


1:6 


From outside dish 


ail 


Sept., 


'05 


1:6 


From inside dish 


a^i 


Sept., 


'05 


1:6 


From outside dish 


ai. 


Oct., 


'05 


1:6 




ai. 


Oct., 


'05 


1:6 





^Samples a, and a-^ not preserved. 



i8 



Bulletin of the Bureau of Standards, 



[ Vol. 4, No. I. 



formed. To prevent mechanical loss the inner dish was covered 
with a perforated crystallizing dish, through which the glass stirrer 
and anode connection passed. A metallic shield attached to the 
shaft of the stirrer prevented possible contamination by oil and 
particles of metal from the bearing. 

Nine samples, of which seven were'preserved, were made in 1904, 
and four others in 1905, using this form of apparatus, which was 
«i p designed to give a white 

product free from finely 
divided mercury, as per 
Table I. The current 
density was kept below 
0.25 ampere per square 
decimeter in the prepa- 
ration of all the sam- 
ples. 

(I)) Electrolytic meth- 
od^ new apparatus, -^\n 
the preparation of the 
remaining samples of 
electrolytic mercurous 
sulphate, the apparatus 
was so modified as to 
permit the use of greater 
current densities, which 
necessitated more effi- 
cient stirring. A layer 
of mercury 3 to 4 cm 
deep, purified as de- 
- Apparatus for Electrolytic Preparation of Mercurous scribed above was 

placed in a batter>' jar 




Sulphate {1905). 



about 12 cm in diameter and 20 cm in depth, and the jar nearly 
filled with dilute sulphuric acid. A piece of platinum foil, about 
3 cm square, in the upper part of the solution served as cathode. 
The foil was welded to a short piece of platinum wire, the other 
end of which was sealed into the end of a short glass tube to serve 
as a mercury connection. A small bulb was blown about the middle 
of the tube, so that it rested in a hole through the glass cover of 



wiurs^ Clark and IVestoft Standard Cells, 19 

the jar. When making samples {b^ to {b^ a simple glass T-stirrer 
revolving close to the surface of the mercury^ was used, connections 
to the mercury anode being made as shown in fig. i. The surface 
of the mercury was soon covered with a dark coating, and in addi- 
tion some of the mercurous sulphate accumulated around the anode 
tube. A second stirrer was then made by attaching near the ends 
of the cross arm short glass rods, flattened to form paddles, which 
dipped into the mercury, so that both the mercury and the elec- 
trolyte could be stirred vigorously (samples b^^^ b^^^ A^). As this 
form of stirrer did not prevent the accumulation of mercurous 
sulphate around the anode tube, a combination stirrer and anode 
connection was constructed. The two cross arms (fig. 2), cc and ee 
were about 3 cm apart, and the lower arm had a short piece of 
platinum wire sealed into each end. The paddles, dd^ made of glass 
rod 2 to 2.5 mm in diameter, flattened at the end, were sealed to the 
cross arm, cc^ and the platinum tenninals,^ thus also making the 
construction more rigid and preventing the platinum wires from 
being broken off during cleaning. Electrical contact was made 
with the bearing of the rotating apparatus by means of a copper 
wire, *, soldered into the lower end of the brass cylinder, a, and 
extending into the cross tube, ee. The latter and the lower part 
of the stem were filled with mercury, and the soldered joint was 
protected from amalgamation by a coat of Khotinsky cement. 
The operation was watched as the speed of the stirrer, driven by 
an electric motor, decreased after the formation of sulphate began. 

The best position of the stirrer is readily determined by trial, and 
is that position in which the mercury is vigorously rotated with- 
out being broken up into small globules. A speed of 100 to 200 
revolutions per minute was employed. 

The product formed was light to dark gray, from the presence 
of finely divided mercury, depending upon the current density, 
strength of acid, and rate of stirring employed, all of which were 
varied between wide limits without appreciably affecting the elec- 
tromotive properties of the product. To minimize the possible 
influence of size of grain the stirring was always continued for some 
hours after interrupting the current. 

The mercurous sulphate, separated from the excess of mercury, 
which interfered with its subsequent washing, by means of a sep- 



20 



Bulletin of the Bureau of Standards. 



\_Vol. 4y No. t. 



arating funnel (using no grease on the stopcock) or by means of a 
pipette, was then transferred to a clean glass-stoppered bottle and 
preserved in the dark under part of the electrolyte employed. 
Further data on the samples prepared by the modified apparatus 
are given in the table below. 

TABLE II. 





Electrolytic Method, New Apparatus. 




Sample 


Made 


Current Density 


Cone, of HsS04 


Remarks 


bi 


Feb., '06 


0.2 amp. 


V=0.25 




b. 




0.2 


0.50 




\ 




0.2 


0.75 




b. 




0.2 


0.25 


• 


b, 




0.2 


0.50 


Poor stirring 


\ 




0.2 


0.75 


. 


\ 




0.5 


0.25 




be 




0.5 


0.50 




b, 




0.5 


0.75 




bio 




1.0 


0.25 




bn 




1.0 


0.50 




b„ 




1.0 


0.75 




b» 




5.0 


0.50 




bu 


Mar., '06 


9.25 


0.25 




bi5 




9.25 


0.50 




bis 




9.25 


0.75 




bn 




8 


1 




bi8 




8 


2 




bi. 




8 


5 




b«, 




0.5 


1 




b« 




0.5 


2 




b„ 




0.5 


5 




b^s 




2 


1 




b24 




2 


2 




b,5 




2 


5 




b« 


Dec, '06 


5.25 


1:6 




b« 




5.25 


1:6 




b« 




5.25 


1:6 




b« 


Jan., '07 


5.25 


1.6 




bao 




5.25 


1:6 




b.1 




5.25 


1:6 





iTaui's^ Clark and Western Standard Cells, 21 

{c) By the action of fuming sulphuric addon metallic mercury^ — 
Pure mercury was placed to a depth of about 3 mm in a porcelain 
dish and covered with four times its volume of fuming sulphuric 
acid, stirring from time to time and keeping the dish covered as 
far as possible on account of the acid fumes evolved. In spite of 
this the hood became filled with fumes. The action began in the 
cold but was greatly accelerated by the heat generated, so that the 
sulphate appeared in crj^stalline form after a few minutes. The 
operation was allowed to continue until action nearly stopped, when 
the reaction product was poured into a large beaker of i: 6 sulphuric 
acid, thoroughly stirred and allowed to settle. To avoid spattering, 
the beaker containing the dilute acid was covered with a perforated 
watch glass and the solution introduced through a narrow-stemmed 
funnel extending almost to the surface of the acid. The sulphuric 
acid was then decanted and the mercurous sulphate transferred with 
a little mercury and 1:6 sulphuric acid to a glass-stoppered bottle. 

(d) By the reaction between mercurous nitrate and sulphuric 
acid. — Mercurous sulphate is ordinarily made by the reaction 
between mercurous nitrate and a soluble sulphate in order to avoid 
the presence of a large excess of free acid. For use in Clark and 
Weston cells precipitation by means of zinc or cadmium sulphate, 
respectively, has been recommended. It is, however, preferable to 
use comparatively strong sulphuric acid and to add the mercurous 
nitrate solution to it in order to avoid possible hydrolysis. 

A concentrated solution of mercurous nitrate was prepared by 
the action of concentrated nitric acid on an excess of mercury. 

Sample d^ was made by adding drop by drop to i liter of almost 
boiling sulphuric acid (^=0.25) 250 cc of the above mercurous 
nitrate solution, stirring continuously. The solution was kept hot 
by the aid of an electric stove. During the reaction, fumes of nitric 
acid were evolved. The product consisted of fairly large, pitted 
and irregular crystals, which were washed and preserved, as described 
above. 

Sample d^ was prepared by adding drop by drop 400 cc of the 
mercurous nitrate solution to a large excess of cold 1:4 sulphuric 

"F. E. Smith: Electrician (lyond.), 55, 857; 1905. 



22 Bulletin of the Bureau of Standards, \,voi. 4, No. /. 

acid continuously stirred with mercury in a large battery jar. The 
sample was then washed by decantation with acid of the same 
strength and preser\^ed as described above. This is practically 
Smith's method b?^ In both cases the stirring was continued over 
night to facilitate the reduction of any mercuric salt present. 

{e) By the action of dilute sulphtiric acid^ containing a small 
afHount of nitric acid^ on mercury, — Six samples were made by this 
method, in which the preparation of mercurous nitrate is avoided. 
The reaction which takes place is that involved in the lyunge method 
for the estimation of nitrates, so that the nitric acid is almost com- 
pletely eliminated from the solution. 

6Hg+iH,SO,+2HNO,^-iHg,SO,-^2NO-\-^H^O 

The rate of the reaction depends on the concentration of the sul- 
phuric acid, the amount of nitric acid present, and the temperature. 
The mercury is contained in a beaker and covered with sulphuric 
acid, the nitric acid added, and the whole stirred vigorously and con- 
tinuously for some time after the disappearance of brown fumes of 
nitrogen peroxide. The product formed is quite gray from the 
presence of finely divided mercury, and after washing several times 
by decantation with 1:6 sulphuric acid it should be transferred to a 
glass-stoppered bottle with some of the acid. The conditions under 
which the various samples were formed are as follows: 

Sample e^ was obtained by vigorously stirring a solution consist- 
ing of 600 cc sulphuric acid (^=0.25) and 20 cc concentrated nitric 
acid with a considerable volume of pure mercury. After a few min- 
utes, before starting the stirring, the mercurous sulphate began to 
separate out at the surface of the mercury. The beaker was then 
heated and the stirring begun. Shortly afterwards fumes of nitrogen 
peroxide began to appear, gradually increasing in volume, and 
finally disappearing. The heating and stirring were continued for an 
hour. The product, which settled rapidly, was in grayish aggregates 
of fairly regular cr>'stals, as seen under the microscope. 

"* For the preparation of mercurous nitrate Smith recommends adding nitric acid 
until aU the mercury has gone into solution. This is inadvisable owing to the 
formation of more or less mercuric nitrate. He also recommends that only enough 
mercurous nitrate solution to neutralize 30 per cent of the sulphuric acid should be 
added. 



w5/frj.] Clark and Weston Standard Cells. 23 

Sample e^ was prepared at room temperature in a similar manner 
with a mixture of 8cx) cc 1:4 sulphuric acid and 10 cc nitric acid. 
The action was very much slower. No cry^stals appeared in two 
hours. The stirring was continued for thirty-six hours and a 
voluminous precipitate of fairly good cr>'stals was obtained. 

Sample e^ was obtained at room temperature with 600 cc i : 2 sul- 
phuric acid and 10 cc concentrated nitric acid. The action was 
much more rapid than in the previous case. 

Sample c^ was prepared by adding to 600 cc 1:4 sulphuric acid, 
previously heated almost to boiling, 2 cc concentrated nitric acid. 
There was no visible action after one hour, even after adding a 
small quantity of electrolytically prepared mercurous sulphate. On 
interrupting the stirring, however, the formation of the mercurous 
sulphate and nitrogen peroxide began almost immediately. 

Sample ^5 w^as prepared in a similar manner, using 750 cc 1:4 
sulphuric acid and 2 cc nitric acid. Crystals very irregular. 

Sample e^ was prepared in the same manner as the previous 
sample except that the solution was not heated and twice the quan- 
tity of nitric acid was used. The action was very slow in starting 
so that after waiting a considerable time the formation was started 
electrolytically by a current of 2 amperes for less than two minutes. 
The crystals were also ver}'^ irregular. 

Samples e^^ ^„ and e^ were tested for nitric acid by brucine. The 
sulphuric acid in which the samples were prepared gave a mere 
trace for sample e^^ a. small quantity for sample ^g, and a consider- 
able quantity in sample e^y the latter two being being prepared in 
the cold. The mercurous sulphate samples showed only mere traces 
of nitrate. 

The same samples and the filtrates were also tested for ammonia 
by means of Nessler's solution, but the results were negative. 

(J^ By reduction of mercuric sulphate by metallic mercury. — 
Mercuric sulphate was prepared by adding 150 grams of pure 
mercury to 350 cc concentrated sulphuric acid, previously heated 
approximately to the boiling point. The heating was continued 
for some time after all the mercury had been dissolved, and the 
white product dissolved in 2.5 liters of 1:6 sulphuric acid, the solu- 
tion remaining perfectly clear. 



24 Bulletin of the Bureau of Standards, \voL4>^'o.i. 

Sample y^ was prepared by vigorously stirring 400 ccof the above 
solution, further diluted to about 2 liters with 1:6 sulphuric acid, 
with metallic mercury. The product formed was quite dark. The 
stirring was continued over night, and in the morning the acid 
showed no trace of mercuric sulphate. 

Sample y^ was prepared in a similar manner with 100 cc of the 
mercuric sulphate solution diluted with nine times its volume of a 
solution of sulphuric acid containing 200 grams per liter. After 
the action seemed completed an additional 100 cc of the mercuric 
sulphate solution was added and the stirring continued over night. 
No mercuric sulphate was found in the solution. 

{g) By reduction of mercuric sulphate with sulphurous acid, — 
A considerable number of experiments were made under varying 
conditions on the action of sulphurous acid on mercuric sulphate. 
In most cases an approximately saturated solution of sulphurous 
acid, diluted with sulphuric acid and water so that the concentra- 
tion of the sulphuric acid was at least 1:6, was introduced drop by 
drop into a similarly diluted mercuric sulphate solution and vigor- 
ously stirred. After some time the solution would become cloudy 
from the formation of mercurous sulphate and on intemipting the 
stirring the white product would collect at the bottom of the beaker. 
On the further addition of H^SO^ the product would become gray. 
The crystals obtained were usually quite large and fairly good. 
Ver>' different results were obtained by mixing the solutions quickly, 
the cr^'^stals being in the form of irregular plates; sometimes feathery 
or large prismatic crystals were obtained. They appeared cloudy 
when examined under the microscope. An excess of sulphurous 
acid should be avoided to prevent the further reduction to metallic 
mercury. 

Sample gy^ was obtained by adding drop by drop a dilute solution 
of sulphurous acid in 1:6 sulphuric acid, to a similarly diluted solu- 
tion of mercuric sulphate, previously heated and continuously stir- 
red. The heating was continued for some hours and the stirring 
over night. The crystals formed were white and fairly regular. 

Sample g^ was prepared in a similar manner, but without heat- 
ing the solution. The crystals obtained were white, but much 
channeled. 



w'S'^jJ Clark and Weston Standard Cells, 25 

Sample g^. Twenty-five grams of chemically pure mercuric sul- 
phate were dissolved in one liter of i : 6 sulphuric acid and reduced 
by means of a slow current of sulphur dioxide, mixed with air, the 
solution being kept at 80? It was then digested in a covered beaker 
for two days at the same temperature. 

HBTHODS OF TREATMENT OF COMMERCIAL SAMPLES. 

In the earlier stages of the work efforts were made to obtain the 
mercurous sulphate in the form of perfect crystals. It was first 
noticed that the character of commercial samples was very consid- 
erably modified by digesting them with 1:6 sulphuric acid on the 
steam bath. The commercial samples were very fine-grained, and 
when examined under the microscope showed hardly any regular 
crystalline structure with the magnification employed, while, after 
digesting, crystals of considerable size and some regularity were 
obtained. This suggested the possibility of obtaining perfect crys- 
tals by slow recrystallization from strong sulphuric acid. On slowly 
cooling long crystals of an acid sulphate were formed, which became 
whitish and opaque when treated with water, alcohol, anhydrous 
ether or even concentrated sulphuric acid, after they had been fil- 
tered by suction. When the solution was rapidly cooled fairly good 
crystals began to separate out when the solution was still quite warm. 

Experiments were next made to precipitate the mercurous sulphate 
from its solution in strong sulphuric acid by gradual dilution with 
sulphuric acid of various concentrations not less than i : 6. 

(Ji) By crystallization front strong sulphuric acid. — Sample Aj was 
prepared as follows: 

Concentrated sulphuric acid was heated to 150° and an excess of 
commercial mercurous sulphate added. Three hundred cc of the 
cloudy liquid was transferred to a beaker and stirred. It did not 
clear on adding fuming sulphuric acid. Three hundred cc of 1:2 
sulphuric acid was added drop by drop. Then about 200 cc of i : 3 
and finally 500 cc of 1:6 sulphuric acid were added in the same 
manner. The precipitated mercurous sulphate was in comparatively 
large crystals, which were, however, much channeled. 

The warm mother liquor was decanted and divided into equal 
portions. To one was added an equal volume of hot water. Both 



26 Bulletin of the Bureau of Standards, ivoi. 4, No. i. 

lots yielded crystals on cooling, those from the diluted portion being 
very perfect. 

Sample A, was prepared by dissolving 50 grams of Kahlbaum 
mercurous sulphate in 250 cc of concentrated sulphuric acid previ- 
ously heated to 150? To the clear liquid was added an excess of 
mercury and 300 cc concentrated sulphuric acid. This was diluted 
by adding drop by drop 600 cc 1:2, 300 cc 1:3, and finally 1,500 
cc 1 : 6 acid. After all the dilute acid had been introduced, it was 
rapidly cooled to room temperature, the mother-liquor decanted, 
and the mercurous sulphate washed twice with i : 6 sulphuric acid. 

(A3) Smith " has also described a method for preparing mercurous 
sulphate by recrystallization from sulphuric acid. This sample was 
made by closely following his specifications. Chemically pure 
mercurous sulphate as purchased was warmed in a covered evapcK 
rating dish with pure concentrated sulphuric acid and a small quan- 
tity of mercury to a temperature of about 150® for about ten min- 
utes, the mixture being kept well stirred. After settling, the clear 
solution was poured into i : 6 sulphuric acid, when crystalline mer- 
curous sulphate separated out. About ten times the bulk of dilute 
acid was employed and, to avoid spitting, the hot liquid was poured 
through a fimnel having its stem immersed in the dilute acid. The 
mixture was well stirred, and after cooling the sulphuric acid was 
decanted and the mercurous sulphate was transferred to a glass- 
stoppered bottle. 

(z\ A, /, w, n) By digestion with sulphuric acid. — Sample i^ was pre- 
pared by heating mercurous sulphate (Kahlbaum B) with mercury 
and concentrated sulphuric acid to 150° for some hours. Compact 
crystals were obtained when the solution was rapidly cooled. 

Sample i^ was one of a large number prepared by heating mercu- 
rous sulphate (Kahlbaum B) with strong sulphuric acid. 

Further experiments were made to study the influence of digest- 
ing commercial samples of mercurous sulphate with dilute sulphuric 
acid under various conditions. Six samples purchased as chemically 
pure were available. Three of these were obtained from Kahlbaum 
at different times and the others from Merck, Schuchardt, and Gehe. 
Twenty-five grams of each of these six samples were digested with 

'^F. E. Smith: Electrician (I^ond.), 55, p. 857; 1905. 



wS'^j.] Clark and Weston Standard Cells. 27 

hot 1:4 sulphuric acid and mercury in March, 1906. The samples 
were ground in an agate mortar with the acid and transferred to a 
1.5-liter beaker and vigorously stirred and heated to about 90° for 
several hours. The stirring was continued until the next morning. 
The Merck sample at first showed a decidedly yellowish color which 
disappeared during the night except above the level of the liquid. 

In some cases the beakers were sheathed with asbestos and 
covered with watch glasses to reduce the formation of the yellow 
incrustation due to the condensation of water on the sides of the 
beaker and its action on the mercurous sulphate. The effect was 
further reduced in one case by blowing air into the beaker through 
a hole in the cover glass to prevent condensation, and by increasing 
the speed of the stirrer from time to time to sweep back any 
mercurous sulphate into the body of the liquid. 

In the tables below these samples are designated as follows: 



Source 


Designation 


Kahlbaum A 


ki 


KahlbaumB 


k. 


Kahlbaum C 


k. 


Merck 


k* 


Schuchardt 


k, 


Gehe 


k. 



Five of the commercial samples were digested with 25 per cent 
sulphuric acid and four of them with 10 per cent acid since April, 
1904. All six samples were digested with 1:6 acid and mercury 
since October, 1905, the bottles being shaken from time to time. 
In the table below these samples are designated as follows : 

Treatment and Designation. 

Sample 25^ acid 10 ;^ acid 1:6 acid 

Kahlbaun A 
KaUbatimB 
Kahlbaum C 
Merck 
Schuchardt 
Gehe 

Samples li to I5 were vigorously stirred (April, 1906) with mer- 
cury and acid for twenty-four hours and then preserved in bottles 
with mercury. 



ll 


m. 


nx 


1. 


-- 


na 


.. 


-- 


% 


13 


ma 


^4 


14 


m3 


Ds 


15 


m. 


06 



28 Bulletin of the Bureau of Standards, [roi. ^, jvo. i. 

Tlie paste, — ^This was always freshly prepared before setting up 
the cells. It is obvious from the irregular pitted character of the 
mercurous sulphate crjstals, as shown under the microscope, that 
the greatest care must be taken in washing the sample to completely 
remove all traces of acid. This was done in a platinum Gooch 
crucible with a disk of hardened filter paper at the bottom. These 
disks were cut to size with a cork borer, warmed for some time w4th 
dilute nitric acid, washed until acid-free with hot distilled water and 
dried. A suflScient quantity of the mercurous sulphate, shaken up 
with the acid under which it was preserved, was poured into the 
crucible, care being taken not to transfer any of the mercur>' which 
interferes with the washing, the acid removed by suction, and the 
salt washed twice with small portions of i:6 sulphuric acid to 
remove possible traces of mercuric sulphate formed by the action 
of air on particles of mercurous sulphate not covered by the acid. 
The acid was removed by the addition of 5 or 6 portions of redis- 
tilled absolute alcohol, care being taken to wash down the sides of 
the crucible. To completely remove the alcohol the sulphate w^as 
then washed three or four times with a saturated solution of zinc or 
cadmium sulphate, according to the type of cell to be set up, taking 
the same precautions as above. If the paste cracked or separated 
from the sides of the crucible more of the wash liquid was added 
and the contents of the crucible thoroughly stirred up before again 
applying suction. After scraping ofiF the upper layer the mercurous 
sulphate was transferred to a small, clean, dr>' beaker, or crucible, 
mixed with one-third to one-half its volume of finely powdered zinc 
or cadmium sulphate cn-stals and suflScient saturated zinc or cad- 
mium sulphate solution to make a moderately thin paste. A large 
excess of zinc or cadmium sulphate crystals in the paste should be 
avoided so that practically every part of the mercury surface will be 
in contact with the mercurous sulphate, thus securing the rapid 
attainment of saturation equilibrium. With white samples of mer- 
curous sulphate, one-third the volume of mercury was added with 
the crystals of zinc or cadmium sulphate in making up the paste. 
To eliminate possible influence of size of grain the paste was stirred 
as little as possible in its preparation. 



IVolff. 1 
IVaters.} 



Clark and West07i Standard Cells, 



29 



THE CELLS. 

For facility in filling and sealing the H type was adopted. The 
size and dimensions, although not affecting the electromotive force 
determine the polarization produced by the passage of a current 
and the rapidity with which the cell assumes the temperature of its 
surroundings. Figure 3, drawn to half scale, gives the approximate 
dimensions of the cells used at the Bureau. Especial care was taken 
in sealing in the platinum wires and subsequent annealing. As 
recommended by Hulett, the platinum wire inside the cell was 
covered in most cases with a thin layer of glass to within i mm or 



n n 



<^nrsTAL«-i 



n n 




Fig- 3. Fig. 4. 

Sectional Views of Standard Cells {Half size). 

less from the end. The wire should not be larger than B. & S. 
No. 28, to reduce the liability of cracking. No. 32 was used in 
most of our cells. 

The Clark cells nevertheless frequently cracked at the point where 
the platinum terminal was sealed into the amalgam limb. This 
may be avoided by a construction recommended by the Reichsanstalt 
and shown in figure 4, in which the platinum terminal of the amal- 
gam limb is sealed into a side tube while the amalgam is still 
liquid, contact being made by sucking the amalgam up into this 
tube. The platinum wire extends downward about 2 cm below the 
8919—07 3 



30 Bulletin of the Bureau of Standards, \voi. 4, No. i. 

point at which it is sealed into the tube and the amalgam should 
cover only its lower half, thus preventing the glass from cracking 
at the seal. This construction also reduces the chance of contact 
between the platinum and the electrolyte, and for this reason is 
preferable for portable cells. This form was adopted, for Clark 
cells, in our later work. 

As the cells are to be sealed off above the cross arm after filling, 
they may be slightly constricted beforehand, but if the wall thick- 
ness is not greater than 0.75 mm, as was the case with our cells, 
this is not necessary. The length of the tube above the cross arm 
as shown in figures 3 and 4, although greater than absolutely neces- 
sary, facilitates the sealing but at the same time somewhat increases 
the difficulty of filling. 

Cleaning the cell. — The cells and filling tubes when badly con- 
taminated with grease, etc., were covered with chromic acid mixture 
and allowed to stand overnight. Longer contact with this cleaning 
mixture was avoided on account of the danger of forming lead 
chromate from the lead sealing-in glass employed.*® The cells were 
then washed with distilled water, filled with aqua regia, which was 
allowed to remain in them for thirty minutes, and repeatedly washed 
with distilled water. The action of the aqua regia on the platinum 
wires facilitated subsequent amalgamation. Ordinarily the cleaning 
with chromic acid mixture could be omitted. 

Amalgamation of the platinum terminals. -^\n order to minimize 
the possibility of contact between the electrolyte and the platinum 
tenninals, especially from shaking in transport, they were amalga- 
mated with a solution of pure mercurous nitrate in dilute nitric 
acid. The amalgamating solution was introduced into the cell and 
a weak current passed through it from a platinum wire anode to the 
platinum terminal externally connected to the negative pole of a 
battery. Sufficient mercury was deposited in a few minutes. In a 
type of portable cell to be described later, the limb intended to 
receive the paste was provided with a platinum foil electrode welded 
to the platinum wire. (Fig. 4.) In this case the whole surface was 

^ This was observed in one lot of cells that had been overlooked and had been left 
in the cleaning fluid for several weeks. The chromate was not removed by treat- 
ment for several days with nitric acid or aqua regia. 



i^a^s^ Clark and Weston Standard Cells, 31 

thoroughly amalgamated, for which a proportionately longer time 
was required. Especial care was taken as the amalgamated foil was 
employed to replace the mercury. 

To remove every trace of the amalgamating solution the cell 
was next washed several times with dilute nitric acid, and finally 
repeatedly rinsed with distilled water. The amalgamated surface 
was usually '' rinsed " with a small quantity of pure mercury, the 
cell then dried in an air bath at 110°. 

Introduction of the materials, — The materials were easily and 
neatly introduced by means of filling tubes, care being taken not to 
allow the latter to come in contact with the walls of the cell. 

The amalgam. — ^The zinc or cadmium amalgam, prepared as 
described above, was heated slightly above its melting point and a 
quantity of it sufficient to cover the platinum terminal to a depth 
of at least 10 mm transferred to the cell by means of a previously 
heated, clean, dry pipette. A pipette with a rounded end, at the 
center of which is a small hole, was found more satisfactory than 
one drawn out to a capillary, which the amalgam tended to clog up 
owing to cooling. After heating the pipette, which was provided 
at the upper end with a rubber tube, it was introduced below the 
surface of the amalgam, meanwhile blowing through it, to avoid 
the introduction of any oxide formed on the surface. A suitable 
amount of amalgam was then drawn into the pipette by gentle 
suction, which was released while the pipette was withdrawn, and 
then applied again sufficiently to prevent any more of the amalgam 
from running out. Particles of the amalgam adhering to the out- 
side were then removed by wiping with filter paper and the pipette 
introduced into the cell to within 2 cm of the bottom. On releas- 
ing the suction the amalgam ran out freely, the amount introduced 
being regulated by again applying suction at the proper moment. 
The pipette was then withdrawn without touching the walls of the 
cell. In our earlier work a thin glass tube of slightly less diameter 
than the cell was used to protect the walls but after some practice this 
was found to be unnecessary. 

Particles of amalgam which in spite of precautions occasionally 
adhered to the cell wall, and which could not exert any influence on 



32 Bulletin of the Bureau of Standards, [I'oi. 4. no. r. 

the electromotive force except when forming an integral part of the 
amalgam electrode and not fully covered with crystals, were removed 
by the aid of a glass rod. Great care was taken to prevent them from 
reaching the other limb and contaminating the mercurj', which 
would of course seriously influence the electromotive force. 

Introduction of the mercury, — ^At first the mercury was introduced 
by means of a pipette drawn out to a very fine capillary, but later a 
sufficient quantity to cover the platinum terminal to a depth of 
least 10 mm was simply poured into the cell, care being taken not 
to introduce any into the amalgam limb. By cautiously tilting 
the cell, air bubbles entrapped under the mercury could easily be 
removed. 

Introduction of the paste, — The paste, prepared immediately before 
setting up the cell as described above, was introduced by means of 
a pipette with an opening 3 to 4 mm in diameter. Its consistency 
was such that it could readily be drawn up into and flow from the 
pipette; and therefore finely crushed zinc sulphate or cadmium sul- 
phate crystals were employed. After filling the pipette with paste 
it was wiped with clean filter paper, and a small amount of the 
paste allowed to flow out. The end of the pipette was then brought 
close to the mercury^ and paste allowed to flow into the limb, to a 
depth of 1.5 to 2 cm, except in the cells first set up, care being taken 
to keep the walls of the cell clean and to avoid trapping air bubbles. 

Introduction of the crystals and solution, — The amalgam and 
paste were next covered to a depth of about i cm with saturated 
zinc sulphate or cadmium sulphate solution, after which pulverized 
zinc sulphate or cadmium sulphate was introduced — ^a little at a 
time to avoid trapping air bubbles — to a depth of 1.5 to 2 cm by 
means of a wide-stemmed funnel. The cell was then filled slightly 
above the cross arm with saturated zinc sulphate or cadmium sul- 
phate solution. 

In order to maintain a concentration equilibrium at all tempera- 
tures to which the cell was likely to be exposed, a saturated solution 
of zinc or cadmium sulphate and a sufficient excess of the corre- 
sponding crystals over the amalgam and in the paste were employed. 
The layer of crystals in the mercury limb was intended as a further 



Bull. Bur. of Standards. 



Vol.4. No. 1. 




Fig. 5. — Finished Cells showing Traveling Contacts and Method of Mounting. 



i^a£s.] Clark and Weston Standard Cells. 33 

precaution against their leaching out of the paste, which may happen 
when the solution is not completely saturated. 

Sealing,*^ — ^The cell was next hermetically sealed by the aid of 
two small horizontal blow-pipe flames applied to the cell wall from 
opposite directions. One limb of the cell was closed by a cork and 
the other by a cork nicked at one side, through which passed a glass 
rod to serve as a handle in drawing it out. The cell was gradually 
heated 2 to 3 cm above the level of the liquid, until the danger of 
cracking had passed, and then held in the flame, rotating mean- 
while, imtil the tube almost collapsed, after which it was closed by 
drawing it out slowly while still in the flame. By judicious heating 
the seal could be nicely rounded by the expansion of the inclosed 
air. The second limb was sealed in a similar manner. The finished 
cell is shown in figure 5. Whenever, in filling the cell, the mate- 
rials accidentally came in contact with the cell wall above the 
cross arm, where it was to be heated in sealing, it was cleaned by first 
wiping with filter paper slightly moistened with distilled water and 
then with dry paper. 

THE COMPARING BATHS. 

The relatively large temperature coefficient of the Clark cells 
made it necessary to provide for automatically regulating their tem- 
perature to within 0.01°. With old cells this regulation must be 
maintained for twenty-four hours or more previous to measurements, 
on account of the hysteresis frequently observed. All comparisons 
were therefore made in electrically heated and controlled kerosene 
baths. 

The baths, 70 cm in diameter and 40 cm deep, were set up in a 
room in the basement of the laboratory, the temperature of which 
was automatically controlled to within i^ 



"Wright and Thompson: Phil. Mag. (5), 16, p. 28; 1883. 
Kahle: Zs. f. Instrk., 13, p. 298; 1893. 
Callendar and Baraes: Proc. Roy. Soc, 62, p. 117; 1897. 
Barnes: Ph3rs.Rev., 10, p. 268; 1900. 
Carhartand Hulett: Trans. Am. Electrochem. Soc., 5, p. 67: 1904. 



34 Bulletin of the Bureau of Standards, \vol 4. i^'o. /. 

by means of a thermostat pneumatically operating dampers in the 
hot and tempered air supply ducts. As there were no windows, the 
cells were also protected against any possible influence of direct or 
even diflusedsun light. 

The constniction of the thermoregulator employed in the baths, 
although not embodying any essentially new features, is described 




Fig. 6. — Comparing baih {sectional view) . 

rather fully below for the convenience of others who may wish to 
undertake standard cell work. 

It consists of a reservoir in the form of a horizontal grid made of 
thin-walled glass tubing, 1.5 to 2 cm in diameter, containing the 
thermometric substance (toluene), the volume changes being trans- 
mitted by a U-shaped connecting tube, ^, filled with mercury to a 
vertical capillar}-, d, (Figs. 6 and 7.) The reservoir, ^, is provided 
with a downward extension, ^, to allow for expansion and contrac- 
tion of the toluene when the regulator is used at widely differing 



tVaters. 



] 



Clark and IVeston Standard Cells. 



35 



Htf~* 



T^l 



fr! 



*—Hg. 



llgr 




-h 



temperatures, thus preventing the toluene from reaching the capil- 
lary. In filling, all air must be removed to eliminate the influence 
of variations in atmospheric pressure on the regulation. The capil- 
lary, ^/, I to 2 mm in diameter, is fused to a wider tube, e (fig. 7), 
to the upper end of which is cemented a _^„ 

bushing, y^ fitting loosely enough to allow for 
the cement. The steel pin, ^, with its upper 
end hollowed out to serve as a mercury cup, 
and passing through yj is fixed in position by 
the set screw, A, and has soldered to its long 
end a fine-pointed platinum wire, t\ Five 
millimeters from the free end of the wire is 
fused a glass bead, ^, to facilitate centering, 
but fitting the capillary loosely enough to per- 
mit the ready passage of mercury in either 
direction. It is advisable to have on the rod, 
^, a small steel collar, /, provided with a set 
screw to facilitate resetting after cleaning the 
capillary, which must be done occasionally. 
One end of a second platinum wire, /, is fused 
into the tube, r, below the capillary, and the 
other end into a small glass tube, m^ attached 
to e by two short glass rods, and serving as a 
terminal cup. 

The side tube, «, connected to ^, as shown, 
to avoid trapping air bubbles when for any 
reason the bath may be allowed to cool con- 
siderably, is provided with a well-fitting stop- 
cock communicating with the small mercury 
reservoir, o. 

The bath is brought approximately to the 
temperature at which it is to be regulated and sufficient mercury 
admitted or withdrawn (by gentle suction applied by means of a 
rubber tube) so as to bring the mercury level near the middle of the 
capillary. The pin, ^, is then adjusted so as to make contact with 
the mercury when the desired temperature is reached, thus energizing 
a 50-ohm relay and increasing the external resistance in series with 



Fig. 7 . — Thermoregulator. 



36 Bidletm of the Bureau of Standards, \yoi. 4, No. i. 

the heating coils in the bath. Although the measurements here 
dealt with were all made at 25°, supplementary cooling had to be 
provided during the summer months, heat being abstracted by means 
of water circulation through a copper coil in the bath. The inlet 
and outlet of the coil were below the surface of the oil to prevent 
condensed moisture from getting into the bath. The flow of water 
was regulated so that somewhat more than enough cooling was 
effected, the difference being made up by electric heating. Owing 
to the variable temperature of the tap water, it was first passed 
through a coil in an ice chest. 

In two of the baths the heating coils (Figs. 6 and 8) consist of 
four Ward-Leonard rheostat units, of advance wire wound in enamel 
on fire-clay tubes. These were mounted one in each quadrant by 
metal clips attached to the walls of the tank, external to the space 
occupied by the cells. In the third bath a grid built up of glass rods 
wound with bare advance wire and then shellacked was employed. 
With a iiovolt supply, a resistance of 80 to 125 ohms provided 
ample heating. 

The external resistance, and if necessary the supplementary ice- 
water circulation, were adjusted so as to maintain the bath about 2° 
below the desired temperature, so that the additional heat supply 
required to produce regulation was as small as consistent with varia- 
tions called for by changes in the room temperature, the effect of 
which was considerably reduced by covering the baths externally 
with sheet asbestos. 

A most convenient and inexpensive form of rheostat, where a sup- 
ply of incandescent lamps of various candlepowers is available, is 
shown in figure 8. The lamps in the two lower sockets determine 
the external resistance during the cooling period. When the relay 
circuit is open all the lamps are in parallel. 

Stirring, — Uniformity of temperature throughout the bath was 
secured by an efficient centrally located stirrer producing an upward 
and rotary circulation. In addition the rectangular stand on which 
the cells were mounted was provided with a sheet metal shield 
extending to within 4 cm of the bottom of the bath (Fig. 6), thus 
directing the circulation and in addition protecting the cells from 
the direct influence of the cooling coil, and also in two of the tanks 
from the heating coils. Measurements made by a platinum ther- 



Wolff. 1 
IVaUrs.} 



Clark and Weston Standard Cells, 



37 



mometer showed that the temperature of the space occupied by the 
cells was ever\'where uniform to well within o.oi°, so that it was 




hardly necessary to employ a grid thermoregulator to integrate the 
temperature of the bath. 



3^ Bullethi of the Bureau of Standards, \vol /, No. i. 

The temperature variation during regulation is of course deter- 
mined primarily by the volume and differential cubical expansion 
of the liquid employed in the thermostat and the diameter of the 
capillary. It is influenced, also, by temperature lag in the regu- 
lator and in the heating coils and by any contamination of the mer- 
cury surface at which contact is made. The lag is reduced by the 
form of regulator employed and by a proper adjustment of the exter- 
nal resistance, so that a minimum increase in the heating current is 
required for regulation. 

The actual range can be calculated as follows: 
Let Wy = rate of heat loss in watts during cooling period 
W^2= added heating in watts for regulation 
/, = cooling period in seconds 
/,=: heating " '' " 
Then 

lV,t, = {JV,^ir,)t,, 
or 

•/, + /, 
Hence IV^ can be calculated. 

The total heat loss in joules during the cooling period or gain 
during the heating period will therefore be 

The temperature range may then be found by dividing this quan- 
tity by the calculated heat capacity of the bath expressed in the 
same units. 

The results thus arrived at are in good agreement with direct 
measurements with a platinum thermometer. 

The cells were mounted (Figs. 6 and 8) on six parallel wooden 
strips, each accommodating i8, and held in place by sheet metal 
clips. The strips were supported by a metal framework, so that the 
electrodes of the cells were 25 cm above the bottom of the tank and 
3 or 4 cm above the level of the grid of the thermoregulator. The 
cells were covered to a depth of at least 2 cm with high-grade 
kerosene. 

Between the cells were mounted hard rubber blocks, each carr>-- 
ing two short copper rods, provided with a pair of holes for mercury' 



If^^j] Clark and Weston Standard Cells, 39 

cups, one for a cell terminal and the other for external connections. 
The holes for the latter purpose were spaced at the same distance 
apart, so that any cell could be put in circuit by inserting a pair of 
stiff contact wires mounted on a hard rubber block. (Fig. 5.) This 
method was preferred on account of possible leakage troubles which 
might arise by connecting together all the positive or negative 
terminals and to facilitate the comparison of any number of cells in 
series. 

Connections to the potentiometer were made by the aid of three 
insulated line wires extending over the baths and to which the 
leads from the contact wires and the potentiometer terminals could 
be connected in any desired manner by the aid of metal clips. 
(Fig. 8.) By this means the measurements were so greatly facili- 
tated that the cells could easily be compared to parts per million at 
the rate of icx) per hour. 

THE ELECTRICAL MEASUREMENTS. 

The measurements given below were all made by means of a 
5-dial Wolff potentiometer of the usual construction having a resist- 
ance of lOjCXX) ohms per volt, the units of the tenth ohm dial cor- 
responding therefore to 10 microvolts. The potentiometer current 
was furnished by a storage cell of ample capacity, which was con- 
tinuously left in circuit and covered with sheet asbestos to reduce 
temperature variations. Under these conditions the current, regu- 
lated by a manganin rheostat, was sufficiently constant for all 
purposes. 

A high sensibility D'Arsonval galvanometer, made by the Wes- 
ton Electrical Instrument Company, was employed throughout. A 
difference of 10 microvolts produced a deflection of at least i mm, 
so that the values could be readily measured to microvolts, even 
with the high resistance potentiometer employed. 

The comparison of cells of the same type was made by the differ- 
ential method, each cell being measured in opposition to one of the 
lot taken as a standard of reference. As the differences measured 
were small, no errors are introduced by possible variations of the 
potentiometer current likely to occur during a complete set of 
measurements. From the differences thus measured the results could 
be expressed in terms of any particular cell or the mean value of a 



40 Btdletin of the Bureau of Standards. \voi, /, No. i. 

number by applying a suitable correction. This method has an 
additional advantage, particularly with Clark cells when in the 
same bath, as all vary simultaneously by an approximately equal 
amount with the minor temperature variations during regulation. 

As a further check on the constancy of both the Clark and Wes- 
ton cells their ratio was determined from time to time, both by the 
direct method in which a number of the cells of each type were 
separately measured and by the differential method in which the 
difference between series of five Clark and seven Weston cells was 
determined. The differential method had the advantage that the 
potentiometer corrections became almost negligible, as did also 
errors due to variations in the potentiometer current. In addition, 
it was practicable to determine the average difference during a com- 
plete cycle of regulation. The result thus obtained gives the mean 
ratio of the cells concerned. 

Temperature fneasurements, — The influence of errors in measur- 
ing the temperature enters only in determining the value of the 
Weston in terms of the Clark cell, as in most of the work all the 
Clark cells were in the same bath. 

The accuracy required in the temperature measurements is deter- 
mined by the temperature coefficient of the Clark cell, almost one- 
tenth per cent per degree, corresponding to o.oi° where an accuracy 
of one part in 100,000 is sought. Mercury thermometers standard- 
ized at the Bureau were employed throughout; some checks have, 
however, been made by a platinum thermometer. In the earlier 
stages of the work less care was devoted to the detennination of the 
Clark- Weston ratio, as new cells of both types were being constantly 
set up, and a single thermometer was used. In a redetermination 
of the temperature coefficients shortly to be made both mercur>' and 
platinum resistance thermometers will be employed. 

Other possible sources of error, — The corrections of the potentio- 
meter employed were determined from time to time to an accuracy 
of at least i part in 100,000. The close agreement of the values of 
Weston in terms of Clark cells obtained by the direct and differen- 
tial methods (Table XVI) shows that no errors larger than the above 
amount can be thus introduced. The agreement also shows no 
appreciable errors are introduced by defective insulation which 
would affect the terminal potentials measured unequally. Measure- 
ments were, however, made of all insulation resistances, including 



H^^uirs^ Clark and Weston Standard Cells. 41 

the resistance between cell terminals in the bath on a blank cell 
with the cross arm sealed off, but in every case the resistances were 
found to be so large as not to introduce an error as great as i part 
in 103,000 in the results. This was surprising, since the oil in two 
of the baths had been contaminated by the breakage of cells. 

Thermoelectromotive forces, always very small, were eliminated 
in the usual manner by a simultaneous reversal of the potentiometer 
current and the connections of the cell circuit. The very small 
variations in the potentiometer current, not affecting the measure- 
ment of the differences between cells of the same type and in the 
differential method were practically eliminated in the direct com- 
parison of Clark and Weston cells by a repetition of the observations 
in reverse order. The possible influence of hysteresis was prac- 
tically eliminated by very close regulation of the baths. 

TABULATION OF RESULTS. 

The following tables give the results of a few of the numerous 
series of measurements on cells set up to test the electromotive 
properties of mercurous sulphate. A considerable number of other 
cells have been constructed for testing the other materials, different 
methods of washing the mercurous sulphate, influence of depth of 
paste, size of g^ain, and other possible causes of variation. A dis- 
cussion of the results obtained, together with a study of the influence 
of added impurities, will be reserved for a later paper, as the mer- 
curous sulphate has been found mainly, if not entirely, responsible 
for the variations observed. 

In Tables III to XV, below, the first column gives the number of 
the cell, the second the date of setting up, the third the designation 
of the mercurous sulphate employed, the letter indicating the 
method of preparation and the subscript the number of the sample 
(see text) ; column four shows which lot of cadmium or zinc sulphate 
was employed, and column five gives similar information in regard to 
the amalgams. In the remaining columns are given the differences 
in microvolts between the individual cells and the mean of a num- 
ber arbitrarily selected as a basis of reference.*' The three undated 
columns, marked *, **, and *** give the differences within one, two, 
and seven days, respectively, after the date of setting up the cells. 

*' Weston cells Nos. i, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, and 15, and Clark cells Nos. 
27a, 28, 32, 34, and 39, data for which are given in heavy type in the tables. 



42 Bulletin of the Bureau of Standards, \voL4^i^'o.i. 

TABLE III. 

Weston Cells. — Electrolytic Mercurous Sulphate made with Old Apparatus. 

[Differences in Microvolts from Mean of Reference Cells.] 




+ 47 I +35 
+ 33 , {34 



+ 56 

+ 41 

+ 87 

+ 66 



+107 
+ 38 



+ 31 
+ 23 



I r 



July 
1906 



+ 57 
+ 39 
+ 92 
+ 67 
+ 13 
+102 



+ 39 
- 9 

+ 68 



+ 68 


+ 50 


+ 46 


+ 26 


+ 25 


+ 11 


+ 32 


+ 29 


+ 11 


- 3 


- 8 


- 14 


- 1 


- 5 


- 9 


+ 19 


+ 13 


+ 5 


- 17 


- 17 


17 



+ 26 
+ 4 
+ 48 



+ 9 

+ 14 

11 

- 6 
+ 9 

- 17 



July 



+ 54 
+ 35 
+ 84 
+ 63 
+ 12 
+ 83 



+ 31 
- 8 
+ 50 



+ 24 

+ 4 
+ 34 



+ 9 
+ 13 
- 10 

+ 9 
16 



Aug. 

4 



Aug. 



+ 47 

+ 34 

+ 78 

+ 58 

+ 14 _ 

+ 74 i + 68 I 



+ 39 
+ 33 
+ 81 
+ 55 
+ 13 



+ 32 
- 6 

+ 45 



+ 28 
- 7 

+ 41 



+ 25 ' + 23 
+ 4 I + 4 
+ 30 I ,29 



+ 9+7 

+ 8 I + 8 

- 10 I - 9 

- 3 I 

+ 4+6 

- 15 - 21 



Haters.} 



Clark and JVeston Standard Cells, 
TABLE III. 



43 



Weston Cells. — Electrolytic Meroirous Sulphate made with Old Apparatus. 
[Differences in Microvolts from Mean of Ref -^rence Cells. ] 



Cell 


Sept. 
13 


Oct. 
13 


Nov. 

a 


Nov. ' 
19 , 


Dec. 

X 


Jan. 
xo, 
igo7 


Mar. 

X 


Mar. 

as 


Apr. 


May 


June 
a6 


July 

23 


" 


f 40 


+ 29 


1 
+ 25 


+ 21 


+ 20 


+ 11 


+ 2 





- 7 


- 5 


-16 


- 18 


76 


+ 27 


+ 24 


+ 19 


+ 18 ' 


+ 16 


+ 7 


- 1 


- 2 


- 10 


- 11 


- 17 


- 18 


64 


+ 73 


+ 71 


+ 68 


+ 66 


-f- 62 


+ 59 


+ 50 


+ 48 


+ 41 


+ 38 


+ 32 


+ 28 


65 


+ 40 


+ 47 


+ 46 


+ 44 


+ 43 


+ 36 


+ 38 


+ 37 


-^34 


+ 35 


+ 31 


+ 30 


8 


+ 12 


+ 12 


+ 11 


+ 10 


+ 12 


+ 7 


+ 11 


+ 11 


^ 9 


+ 9 


+ 8 


+ 8 


40 


+ 65 


+ 63 


+ 56 


+ 49 


+ 46 


+ 35 


+ 24 


+ 18 


+ 10 


+ 3 


~ 9 


- 14 


8a 






















+147 


+ 65 


66 


+ 25 


+ 24 


+ 21 


+ 22 


+ 19 


+ 18 


+ 18 


+ 19 


+ 14 


+ 14 


+ 10 


+ 10 


9 


+ 2 


5 


- 6 


- 4 


- 7 


(-29)1 














41 


-h 44 


^ 48 


+ 47 


+ 38 


+ 36 


•+ 27 


+ 33 


+ 33 


+ 30 


+ 29 


+ 22 


+ 23 


9a 
67 






















+ 47 
^ 12 


+ 15 


+ 20 


+ 20 


+ 20 


+ 20 


+ 18 


+ 16 


+ 18 


+ 15 


+ 15 


+ 14 


+ 15 


11 


+ 3 


+ 3 


+ 3 


f- 2 


+ 1 


+ 2 


+ 1 


+ 3 


r 1 


+ 2 








42 


4- 30 


+ 33 


+ 31 


+ 25 


+ 26 


+ 24 


+ 25 


+ 25 


0) 








na 
68 




















+ 68 
- 19 


+ 23 


+ 3 


+ 2 


- 1 


- 3 


- 6 


- 9 




- 13 


- 16 


- 17 


- 19 


70 


+ 3 








+ 1 


- 3 


- 4 


- 7 


- 7 


- 9 


- 7 


- 9 


- n 


71 


- 11 


- 11 


- 10 


- 10 


- 10 


- 13 


- 14 


- 12 


-16 


- 15 


- 17 


- 15 


72 
73 










- 5 
+ 1 


- 6 

- 1 


- 9 



~ 10 

- 1 


- 14 

- 3 


- 13 



- 13 



- 15 


+ 2 


i + 3 


+ 1 




+ 2 


- 5 


74 


- 20 


\-'' 


- 26 

1 


- 23 


- 18 


- 20 


- 23 


- 24 


-19 


- 20 


- 22 


- 22 



' oil in cell; seal found defective. 



44 



Bulletin of the Bureau of Standards. 



[Vol. 4, No. I. 



TABLE IV. 



Weston Cells. — Electrolytic Mercurous Sulphate made with New Apparatus. 

Concentration of Sulphuric Acid exceeding Gram-Molecular. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 



Date 



26 
51 
27 
52 
28 



3 

3a 
29 
30 
46 
46a 
46b 
31 
47 



6 

6a 
6b 

151 
5 

14 

37 
15 

38 

15a 

178 
179 
180 



I May 9, '06 

June 23, '06 

I May 9, »06 

June 23, '06 

May 9, '06 



61 June 25, '06 

62 ** 
63 



Mer 

curous 
sul- 
phate 



May 11, '06 

June 25, '07 

May 9, '06 

June 23, '06 

June 25, '06 

June 25, '07 

May 9, '06 

June 23, '06 



4 I May 11, '06 

4a June 25, '07 

32 May 9, '06 
33 

June 23, '06 

May 9, '06 

June 23, '06 



May 11, '06 

Dec. 3, 06 



Dec. 15, '06 
May 11, '06 
May 16, '06 
May 9, '06 
May 16, '06 
May 9, '06 
June 25, »07 

Dec. 21, '06 



bi 

l>4 

b6 
bs 

br 

b« 

bs 
bs 
bs 
b. 
b» 

bio 
bio 
bio 
bii 
bii 
bis 
bi2 

bi, 

bi, 
bii 

bi« 
bi4 
bi6 

bi6 
bie 
bie 
bi. 

b» 
br 
bu 



CdSb4 



ai 
ai 
ai 
ai 

ai 
ai 
ai 

■i 
as 
ai 
ai 
ai 
ai 
a« 
ai 
ai 

«i 
a« 

ai 
ai 
ai 
ai 
ai 

«i 
a« 
aa 

ai 

«i 
•i 
ai 
«i 
ai 
a« 

a« 

aa 
aa 



Cd 
Amal- 
gam 



b 
b 
b 
b 
b 

b 
b 
b 

b 

b 
b 
b 
b 
b 
b 
b 
b 

b 

b 
b 
b 
b 
b 
b 

b 

a 
a 

b 
b 
b 
b 
b 
b 
b 

a 
a 
a 



+14 



+12 
+ 7 
- 1 



+12 

+ 7 




+18 



+ 4 



+29 



+ 8 



- 7 
-10 



+30 



+24 
- 6 
+ 10 



+12 

+ 7 
+ 8 
- 8 



- 8 



+28 



+ 1 
- 1 
-11 



+ 4 



+18 
-16 

+ 9 



- 6 

- 3 



-10 

- 9 

- 5 



+11 

+ 8 
+10 
- 9 



July 
X906 



+ 24 

- 12 

- 3 
+ 19 
+ 35 

+ 4 

- 1 

- 8 



July Aug, 



+ 14 I + 12 

- 10 I - 10 

- 4 I - 4 
+ 14 ' + 12 
+ 28 j + 22 

+ '2+1 
+ 1 j 

-9-9 



+ 41+4+4 



+ 21 

+ 12 

-^ 17 

- 16 



+ 15+12 
+ 5 I -+ 3 
+ 16 



+ 18 ' 



16 ' - 15 



I 



+ 23 
+ 2 

- 7 



- 18 
+ 7 

- 7 

- 14 

- 6 

-12 



+ 16 
+ 2 

- 6 



- 20 
+ 5 

- 9 
+ 10 

- 7 

-12 



+ 13 




- 23 
+ 3 

- 10 

+ 7 

- 6 



Aug. 
ax 



+ 10 

- 9 

- 7 
+ 9 
+ 18 

+ 1 


- 12 

+ 3 



+ 10 

+ 1 

+ 17 

- 18 



+ 10 


- 6 



- 22 

+ 2 

- 8 
+ 7 

- 8 



10 -11 



Given to Prof. Hulett 



I 





- 5 

- 7 
-14 

- 5 



- 1 

- 2 

- 6 
-14 

Given to Prof. 





- 1 

- 8 
-13 



- 1 

- 1 

- 6 
-15 

Hulett 



1 



I 



wa^j.] Clark and Weston Standard Cells, 45 

TABLE IV. 

Weston Cells. — Electroljrdc Mercurous Sulphate made with New Apparatus. 

Concentration of Sulphuric Add exceeding Gram-Molecular. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell i ^^*- 


Oct. 

13 


Nov. 

a 


Nov. 
19 


Dec. 

I 


Jan. 
X907 


Mar. 

X 


Mar. 
«5 


Apr. May 
94 34 


June 
96 

+ 5 

- 13 

- 8 

- 3 

+ 9 



- 8 

- 11 

+ 9 
+ 18 
+ 10 
+ 1 
+ 6 

- 21 
+ 29 
+ 4 

- 10 

- 6 
+ 8 

- 34 



- 14 
+ 4 

- 13 

-10 

- 16 

- 7 
+ 2 

- 2 

- 3 
-16 


July 
a3 


26 
51 
27 
52 
28 

61 
62 
63 

3 
3a 

29 
30 
46 

46a 

46b 


+ 10 

- 12 

- 6 
+ 4 
+ 18 

+ 2 

- 4 

- 11 

+ 5 


+ 12 

- 11 

- 5 

+ 4 
+ 18 

- 2 

- 4 

- 9 

+ 5 


+ 15 

- 12 

- 3 
+ 4 
+ 21 

- 1 

- 5 

- 9 

+ 4 


+ 11 

- 10 

- 4 
+ 2 
+ 16 

- 1 

- 6 

- 8 

+ 4 


+ 13 

- 11 

- 4 
+ 1 
+ 18 

+ 1 

- 4 

- 8 

+ 1 


+ 6 

- 11 

- 3 
+ 3 
+ 18 

- 2 

- 2 

- 8 

+ 5 


+ 10 

- 12 

- 3 

- 1 
+ 17 

- 1 

- 7 

- 9 

+ 7 


+ 10 

- 12 

- 4 


+ 17 

+ 1 

- 6 
" 10 

+ 6 


+ 7 

- 12 

- 6 

- 11 
+ 14 



- 6 

- 10 

+ 7 


+ 6 

- 13 

- 7 

- 2 
+ 13 

- 1 

- 7 

- 12 

+ 6 


+ 3 

- 15 

- 9 

- 3 

+ 9 

- 3 

- 9 

- 13 

+ 8 

- 3 


+ 11 
+ 1 
+ 14 
- 19 


+ 12 
+ 1 
+ 14 
- 17 


+ 15 
+ 6 
+ 11 
- 20 


+ 12 

+ 3 
+ 13 
- 17 


+ 14 
+ 3 
+ 12 
- 16 


+ 9 
+ 4 
+ 7 
- 16 


+ 11 
+ 1 
+ 8 
- 18 


+ 13 
+ 4 
+ 10 
- 20 


+ 12 
+ 1 
+ 7 
- 17 


+ 13 
+ 1 
+ 7 
-20 


+ 9 

- 1 
+ 6 

- 17 

- 5 


31 

47 

4 

4a 


+ 10 

- 2 

- 6 


+ 9 

- 1 

- 6 


+ 14 
- 2 

- 7 


+ 10 

- 1 

- 7 


+ 11 

- 1 

- 6 


+ 11 

- 3 

- 7 


+ 9 

- 5 

- 5 


+ 11 

- 6 

- 9 


+ 7 

- 8 

- 7 


+ 6 

- 8 

- 7 


+ 1 

- 14 

- 6 

- 10 


32 
33 
48 

34 
49 

6 

6a 


- 21 

+ 1 

- 11 
+ 7 

- 9 

-11 


- 26 



- 10 
+ 7 

- 9 

-10 


- 11 
+ 5 

- 11 
+ 10 

- 10 

-12 


- 24 
+ 1 

- 11 
+ 6 

- 8 

-10 


- 24 

+ 5 

- 9 
+ 9 

- 8 

- 9 


- 24 

+ 1 

- 11 
+ 5 

- 10 

-11 

- 14 

- 2 

- 3 

- 2 

- 3 
-14 


- 30 

- 1 

- 12 
+ 7 

- 11 

- 9 

- 14 

- 10 
+ 3 

- 1 

- 4 
-17 


- 33 



- 10 
f 10 

- 10 

- 9 

- 12 

- 8 
+ 2 

- 1 

- 1 
-16 


- 30 

- 1 

- 13 
+ 6 

- 13 

- 9 

- 14 

- 7 
+ 2 

- 1 

- 3 
-16 


- 35 

+ 1 

- 12 
+ 7 

- 11 

- 9 

- 13 

- 4 
+ 3 

- 1 

- 3 
-17 


- 34 

- 3 

- 15 
+ 3 

- 14 

- 8 

- 15 


6b 

151 

B 
U 
37 
IS 

38 
















- 3 

- 6 
-18 


- 3 

- 2 

-16 




- 2 

- 2 


- 1 


- 5 
-16 


- 1 

- 2 

- 2 
-13 


+ 2 

- 2 

- 2 
-18 


ISt ' 




i 
















+ 30 

+ 14 
+ 11 
- 8 


- 5 


178 




1 






+ 15 
+ 21 
- 7 


+ 13 
+ 17 
- 12 


+ 13 
+ 18 
- 10 






+ 11 


199 i 








+ 5 


180 ', 












- 11 



8919—07- 



46 



Bulletin of the Bureau of Standards. 
TABLE IV— Continued. 



\_Va.4,No, /. 



Qell 


Date 


Mer- 

curoua 
sul- 
phate 


Cd804 


Cd 
Amal- 
gam 


« 


«« 


•** 


July 
1906 


July 

90 


Aug. 

4 


Aug. 
ax 


190 


Jime 25, '07 
i< 

BzchangeSi 
May 16, '06 

May 9, '06 
Dec. 3, '06 

i« 

Dec. 15, '06 
June 25, '07 


1>M 


A. 




+24 
- 1 
+ 1 


+20 




+ 6 

- 8 

- 4 










191 


b>n > A- 


r ' ' 






192 


imples 
Hu- 
lett's 1 

11 

Hu- 

lett'sn 

(( 

<< 

(< 
Gutlie 


as 
as 










12 


+26 

+ 42 


+27 

A- 36 


+29 

-1- 38 


r28 

+ 39 
ett 


39 








141 

I4ia 




+ 4 

+13 

+12 

+48 


- 3 

+42 


- 4 

- 6 


+ 5 
+30 


Given to Prof. Hal 

1 


141b 
142 


1 

Giyen to George Washington 

UnlYereity 
1 1 


1<J9 




1 








.. .| . 





TABLE V. 

Weston Cells. — Electrolytic Mercurous Sulphate made with New Apparatus. 

Concentration of Sulphuric Add, Gram-Molecular or Less, 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Date 


Mer- 
curous 

sul- 
phate 


Cd804 


Cd 

Amal- 
gam 


* 


«« 


•** 


July 
1906 


July 
ao 

+ 6 
+29 
+13 

- 1 

+ 9 
+17 

+19 

- 8 
+28 
+ 6 


Aug. 

4 


Aug. 
%t 

- 4 

+19 
+ 7 

- 4 
+ 5 

+16 

+14 

- 9 
+17 

- 2 


50 
53 
54 

55 
56 

57 

58 
69 
59 
60 


June 23, '06 
June 25, '06 


1>» 
bfi 

D» 

biT 

IhT 

bis 

b,» 


ai 
ai 
ai 

ai 
ai 

ai 

ai 
ai 

ai 
ai 


b 

b 
b 

b 
b 
b 

b 
b 
b 
b 


+ 7 
+58 
+20 


+19 
+24 
+14 

- 3 

+ 4 
+17 

+45 
+ 5 
+54 
+20 


+12 
+25 
+11 

- 5 
+ 3 
+15 

+27 

- 6 
+34 
+ 6 


+ 9 
+23 
+11 

— 4 
+ 5 
+17 

+24 

- 5 

+34 
+ 6 


+ 2 
+22 
+11 

- 3 

+ 7 
+18 

+17 
-17 
+19 

- 3 



IVaters.} 



Clark and Weston Standard Cells. 
TABLE IV— Continued. 



47 



1 

Cell 


Sept. 
X3 


Oct. 

X3 


Nov. 

a 


Nov. 
19 


Dec. 

z 


Jan. 
xo, 
Z907 


Mar. 

z 


Mar. 

as 


Apr. 
24 


May 

24 


June 
a6 


July 
as 


190 


! 1 1 












+ 24 
- 1 

+ 1 


- 5 


191 


1 1 ' ' 1 


- 17 


192 


! i 






1 


- 15 


12 


+ 26 


+ 28 


+ 29 


+ 30 


+ 28 


+ 32 


+ 30 


+ 31 


+ 31 


+ 31 


+ 31 


+ 32 


39 


+ 37 


+ 38 


+ 38 


+ 42 


+ 35 


+ 39 


+ 39 


+ 40 


+ 37 


+ 35 


+ 36 


+ 34 


141 

14la 
141b 


































- 3 


- 3 


- 3 


- 3 


- 2 


- 1 


- 3 


GlTen to George Washing 
Unhreraity 


on 




142 




+ 4 


- 2 


- 2 


- 3 





- 4 
+ 48 




189 


1 


+ 25 




1 1 1 1 


1 




1 





TABLE V. 

Weston Cells. — Electrol5^c Mercurous Sulphate made with New Apparatus. 

Concentration of Sulphuric Acid, Gram-Molecular or Less. 

[Di£Ferences in Microvolts from Mean of Reference Cells.] 



Cell 


Sept. 
13 


Oct. 

X3 


Nov. 

a 


Nov. 
19 


Dec 

z 


Jan. 
xo, 
1907 


Mar. 

I 


Mar. 
as 


Apr. 

a4 


May 


June 
a6 


July 
as 


so 


- 1 


- 4 


- 1 


- 3 


- 3 


- 5 


-10 


- 8 


-11 


-10 


-13 


-15 


S3 


+18 


+17 


+19 


+18 


+18 


+ 6 


+15 


+18 


+16 


+16 


+15 


+15 


54 


+ 9 


+10 


+11 


+ 9 


+12 


+ 3 


+ 8 


+11 


+10 


+10 


+10 


+ 8 


55 


- 1 


+ 1 


+ 2 





+ 1 


- 1 





+ 2 


+ 2 


+ 2 


+ 1 


- 2 


56 


+ 5 


+ 7 


+ 8 


+ 4 


+ 6 


+ 2 


+ 8 


+11 


+ 9 


+10 


+10 


+ 8 


57 


+15 


+18 


+17 




+16 


+15 


+18 


+20 


+18 


+19 


+20 


+18 


58 


+10 


+13 


+10 


+ 7 


+ 9 


+ 9 


+10 


+12 


+11 


+12 


+10 


+ 9 


69 


- 9 


- 8 


-10 


-- 9 


- 9 


-11 


-12 


-11 


-11 


-11 


-11 


-14 


59 


+13 


+14 


+ 11 


+ 8 


+ 8 


+ 4 


-4 


- 6 


-12 


-16 


-23 


-22 


60 


- 6 


- 6 


- 8 


-10 


- 8 


-12 


-12 


-12 


-13 


-14 


-16 


-15 



48 Bulletin of the Bureau of Standards. ivoi, /, m. i. 

TABLE VI. 
Weston Cells — Chemically Prepared Mercurous Sulphate. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Date 


Mer. 

curoua 
■ul. 
phate 


Cd804 


Cd 


+ 4 


♦♦ 


««* 


July 
5» 
Z906 


July 

ao 


Aug. 

4 


Aug. 

+ 5 


86 


Joaa 


26/06 


c 


«i 




+ 4 


- 5 


+ 1 


+ 3 


+ 4 


99 


Joaa 


27,»06 


di 


*i 




+ 51 


+38 


+20 


+21 


+13 


+ 7 ■ + 5 , 


99a 


Jane 


28, '06 


di 


*i 




+ 13 


+ 2 


- 9 


- 7 


-11 


-16 


-15 


84 


Jaaa 


26, '06 


d« 


*i 




- 11 


-14 


-16 


-17 


-18 


-15 


-18 


84a 


Dee. 


3/06 


de 


•• 




- 19 


-17 


-16 






1 


84b 




f f 


d« 


As 




- 15 


-16 


-16 


Ghren to Geoise Waalilncton 
Unl'?0r8ity 


1 


May 


11/06 


e-, 


a, 




- 9 






+ 7 ! - i 


_ 1 , -« 1 


43 


May 


9/06 


ei 


ai 










— 6 


— 9 


— 11 


—10 


157 


Dec. 


15/06 


•i 




+ 23 




- 3 




- 5 










•la 


June 


25/07 


ei 


Ik: 




+ 47 


+32 


+27 










103 


June 


27/06 


•i 


*i 




- 14 


-16 


-22 


-21 


-22 


■-23" 


-24 


2 


May 


11/06 


e^ 


ai 










- 4 


— 3 


- 2 


- 8 


44 


May 
June 


9/06 




a. 






— 4 


- 6 


_ 5 


— 3 


104 


27/06 




- 17 


-18 


-20 


-16 


-14 


-13 


-13 


2a 




<i 


es 






+ 32 


+17 


+11 










105 1 


If 


«4 


. 


+ 3 


- 5 


-13 


-11 


-11 


-12 


-15 


106a; June 


28/06 


es 


ai 




- 9 


-11 


-15 


-15 


-17 


-22 


-18 


107 




It 


«. 


ai 




- 11 


-15 


-16 


-16 


-18 


-25 


-22 


96 


June 


27/06 


«. 


a, 


b 


- 4 


- 7 


-10 


-12 


-10 


-11 


- 8 : 


97 




it 


^ 


Al 




- 4 


- 7 


- 7 


- 9 


- 8 


-10 


- 9 


100 


June 


27/06 


gi 


ai 




+ 26 


+15 


- 4 


- 4 


-17 


-17 


-17 


looa 


June 


28/06 


Ci 


ai 


b 


+ 66 


+43 


+22 


+22 


+12 


+ 3 


+ 2 


101 


June 
June 


27/06 
28/06 


Si 


ai 
ai 




+121 
+112 






1 






lOla 


+92 


+78 


+78 1 +59 


+51 +48 


163 


Dee. 


15/06 


& 


at 


a 


+102 


+81 


+71 







95 




It 


hi 


ai 




+ 1 


-10 


-23 


-23 -26 


-20 -27 


96 




tt 


m 


ai 




+ 32 


+19 


+ 2 


+ 2 ] + 2 


- 1 - 2 


85 


June 


26/06 


n. 


ai 


1> 


+ 4 


+ 1 


- 6 


- 7 - 7 


-10 1 -12 



Waiers.A 



Clark and IVeston Standard Cells. 

TABLE VI. 

Weston Cells — Chemically Prepared Merciirous Sulphate. 

[Differences in Microvolts from Mean of Reference Cells.] 



49 



CeU ^P*- I ^^^• 
X3 , X3 



Nov. Nov. 
a zg 



86 +3 
99 

99a -18 
84 , -18 

84a 

84b 



+ 4 
~ 2 
-16 
-19 



+ 1 



3 I - 



-21 



Dec. 

z 




- 5 
-14 
-18 



Jan. 

lO, 

1907 


Mar. 

I 


Mar. 
as 


Apr. 


May 


June 
96 


- 2 


- 3 


- 4 


" 7 


- 5 


- 7 


- 4 


-10 


-11 


-13 


-13 


-14 


-15 


-18 


-18 


-19 


-20 


-20 


-19 


-27 


-30 


-27 


-33 


-33 


-16 


-20 


-18 


-18 


-21 


-19 



July 
as 



- 9 
-16 
-18 
-30 
-19 



Given to George Waahincton Unlvenity 



1 

43 
157 


-3 

-11 


-3 

-11 


-4 


-4 
-11 


-5 

-8 


-4 
- 5 
-10 


-4 
-11 
-19 


- 9 

- 9 
-20 


- 8 

-11 
-15 


-5 

- 7 
-15 


-5 

-12 
-19 
+47 
-29 


- 3 
-10 
+32 

[hBoioin 
-23 
-54 

- 9 
-11 

-22 

- 2 


-5 

-15 
—19 


^a 


1 








+ 9 


103 

2 

44 

104 

2a 


-24 ' -26 
-2 -2 

- 3 - 3 
-15 -12 


-25 
-3 
- 3 
-14 


-23 
-3 
- 1 
-11 


-20 

-4 

- 2 

- 9 


-23 

-2 
1- 1 
- 8 


-23 


- 3 
-12 


-26 



- 3 

-10 


-23 

- 1 

- 3 
-10 


-25 
-2 

-10 


-25 
-2 

- 7 
-12 

— 2 


105 
106a 

107 

96 
97 

100 

looa 

101 


-16 
-18 
-21 

:: 

-20 



-16 
-18 
-22 

- 7 

- 8 

-22 




-20 

- 9 
-10 

-21 


-17 
-20 
-23 

- 8 
-10 

-19 



-14 
-16 
-19 

- 6 

- 9 

-16 



-15 
-18 
-27 

- 5 

- 7 

-20 

+ 3 


-19 
-19 
-33 

- 9 

- 9 

-20 

- 3 


-18 
-20 
-39 

- 6 
-10 

-20 

- 1 


-18 
-19 
-46 

- 7 
-13 

-19 

- 1 


1 
-19 
-51 

-10 

-14 

+ 3 


1 
-19 
-52 

-14 
-14 

-19 
- 3 


lOUl 
163 


+43 


+43 


+40 


+40 


+41 


+42 
+39 

-28 
- 4 
-15 


+36 
+14 

-29 

-10 

20 


+36 1 +38 +39 
+14 ' 4-10 -4- 9 


+31 

+ 4 

-29 
- 8 
-28 


+25 
+ 3 


95 
96 
85 


-28 
- 5 

-13 


-28 
- 4 
-12 


-28 

- 4 
-13 


-24 
- 7 
-14 


-24 
- 5 

-11 


-27 
- 7 
-23 


-28 
- 9 
-20 


- 6 
-27 


-28 
-12 
-27 



50 



Bulletin of the Bureau of Standards. 
TABLE VII. 



[l'ol.4,No.i. 



Weston Cells — Specially Treated Commercial Samples of Mercurous 

Sulphate. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Date 


Mer. 

curoua 
sul- 
phate 


Cd804 


Cd 
amalff. 


* 


** 


«** 


July 
1906 


July 


Aug. 

4 


1 

Aug. 
ax 


93 


j™ 


27, '06 


Ii 


+ 44 


+ 29 


+ 14 


+ 14 


+ 12 


+ 8 


+ 9 


94 




<< 


U 


*i 




+ 24 


+ 13 


+ 5 


+ 5 


- 2 








78 


June 


28, '06 


ki 


*i 




- 22 


- 24 


- 19 


- 19 


- 18 


- 22 


- 18 


79 


Juae 


26, '06 


k> 


*i 




+ 10 


+ 8 


+ 5 


+ 4 


+ 5 


+ 4 


+ 6 


80 




it 


ks 


*i 




+ 15 


+ 16 


+ 18 


+ 19 


+ 23 


+ 21 


+ 22 


81 




it 


k« 


ai 




+ 6 


+ 4 


- 1 


- 1 


+ 2 








82 




tt 


k6 


*i 




+ 13 


+ 13 


+ 9 


+ 10 


+ 14 


+ 15 


+ 14 


83 




*t 


k, 
li 


ai 




+ 17 


+ 16 








+ 2 


+ 6 


108 


June 


27, '06 




+ 6 


+ 4 


+ 1 


+ 4 


+ 7 


+ 8 


+ 8 


116 


June 


28, '06 


If 


*i 




+ 51 


+ 51 


+ 49 


+ 54 


+ 55 


+ 50 


+ 51 


109 


June 


27, '06 


1. 


*i 




+ 11 


+ 4 


- 3 





+ 4 


+ 5 


+ 5 


114 


June 


28, '06 


I4 


*i 




+ 54 


+ 64 


+ 55 


+ 61 


+ 59 


+ 52 


+ 54 


115 




<< 


h 


Al 




+ 39 


+ 40 


+ 36 


+ 41 


+ 34 


+ 34 


+ 35 


117 


June 


28, '06 


m, 


*1 




+ 34 


+ 25 


+ 19 


+ 28 


+ 28 


+ 24 


+ » 


119 




<< 


m. 


*I 




+ 24 


+ 15 


+ 17 


+ 17 


+ 23 


+ 19 


+ 24 


118 




tt 


m. 


*l 




+ 79 


+ 75 


+ 71 


+ 79 


+ 79 


+ 75 


+ 76 


120 




tt 


m4 


Al 




+ 76 


+ 75 


+ 69 


+ 78 


+ 78 


+ 74 


+ 76 


87 


June 


27, '06 


tti 


*1 




+ 36 


+ 33 


+ 29 


+ 33 


+ 39 


+ 40 


+ 42 


88 




it 


n. 


*1 




+ 78 


+ 74 


+ 73 


+ 72 


+ 76 


+ 80 


+ 80 


89 




<i 


ii< 


*1 




+114 


+108 


+103 


+107 


+112 


+113 


+112 


90 




n 


nt 


*1 




+ 24 


+ 19 


+ 15 


+ 18 


+ 22 


+ 20 


+ 22 


91 




11 


n* 


*1 




+123 


+123 


+117 


+118 


+124 


+123 


+ 122 


92 




tt 


_^"* 


*1 




+ 74 


+ 73 


+ 74 


+ 73 


+ 71 


+ 68 


+ 67 



iVaters.A 



Clark and Weston Standard Cells, 
TABLE VII. 



51 



Weston Cells — Specially Treated Commercial Samples of Mercurous 

Sulphate. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Sept. 


Oct. 


Nov. 


Nov. 


Dec. 


Jan. 
1907 


Mar. 


Mar. 


Apr. 


May 


June 


July 




13 


13 


3 


X9 


z 


z 


95 


24 


24 


a6 


n 


93 


+ 5 


+ 6 


+ 4 


+ 5 


+ 4 


+ 6 


- 2 





- 2 


- 2 


- 3 


- 4 


94 


- 5 


- 3 


- 5 


- 6 


- 6 


- 5 


- 12 


- 10 


- 13 


- 15 


- 18 


- 18 


78 


- 20 






- 19 


- 15 


- 17 


- 20 


- 22 


- 23 


- 30 


~ 33 


- 30 


79 


+ 3 


+ 5 


+ 5 


+ 5 


+ 3 


+ 7 


+ 3 


+ 3 








- 5 


- 10 


80 


+ 21 


+ 24 


+ 25 


+ 28 


+ 27 


+ 28 


+ 26 


+ 25 


+ 24 


+ 25 


+ 24 


+ 22 


81 


- 1 


+ 1 





+ 1 





+ 2 


- 1 


- 1 


- 1 


- 2 


-- 4 


- 7 


82 


+ 12 


+ 14 


+ 14 


+ 15 


+ 14 


+ 16 


+ 12 


+ 13 


+ 12 


+ 12 


+ 11 


+ 8 


83 





+ 8 


+ 5 


+ 8 


+ 8 


+ 16 


+ 15 


+ 15 


+ 16 


+ 15 


+ 10 


+ 7 


106 


+ 5 


+ 7 


+ 5 


+ 7 


+ 4 


+ 11 


+ 3 


+ 4 


+ 4 


+ 2 


- 9 


- 12 


116 


+ 51 


+ 60 


+ 54 


+ 50 


+ 52 


+ 55 


+ 50 


+ 51 


+ 51 


+ 52 


+ 50 


+ 48 


109 


+ 3 


+ 7 


+ 5 


+ 3 


+ 5 


+ 9 


+ 3 


+ 3 


+ 3 


+ 1 


- 13 


- 25 


114 


+ 54 


t+64 


+ 59 


+ 57 


+ 59 


+ 64 


+ 59 


+ 55 


+ 61 


+ 60 


+ 59 


+ 55 


115 


+ 32 


t+ 42 


+ 35 


+ 31 


+ 32 


+ 35 


+ 30 


+ 30 


+ 31 


+ 30 


+ 23 


+ 4 


117 


+ 28 


t+37 


+ 31 


+ 28 


+ 26 


+ 31 


+ 23 


+ 21 


+ 21 


+ 13 


+ 11 


+ 9 


119 


+ 22 


t+33 


+ 26 


+ 27 


+ 24 


+ 31 


+ 26 


+ 28 


+ 26 


+ 28 


+ 27 


+ 21 


118 


+ 78 


t+87 


+ 84 


+ 81 


+ 83 


+ 86 


+ 83 


+ 85 


+ 86 


+ 86 


+ 86 


+ 82 


120 


+ 74 


t+84 


+ 79 


+ 76 


+ 78 


+ 79 


+ 75 


+ 76 


+ 76 


+ 77 


+ 74 


+ 72 


87 


+ 39 


+ 41 


+ 40 


+ 39 


+ 41 


+ 42 


+ 36 


+ 35 


+ 35 


+ 29 


+ 22 


+ 21 


88 


+ 75 


+ 77 


+ 77 


+ 79 


+ 78 


+ 81 


+ 76 


+ 77 


+ 78 


+ 80 


+ 77 


+ 74 


89 


+108 


+111 


+109 


+110 


+110 


+113 


+106 


+108 


+107 


+110 


+107 


+103 


90 


+ 20 


+ 23 


+ 21 


+ 22 


+ 24 


+ 28 


+ 23 


+ 24 


+ 25 


+ 26 


+ 22 


+ 19 


91 


+ 118 


+120 


+119 


+121 


+120 


+ 124 


+120 


+121 


+122 


+124 


+121 


+119 


92 


+ 65 


+ « 


+ 65 


+ 65 


+ 64 


+ 73 


+ 69 


+ 69 


+ 70 


+ 71 


+ 69 


+ 67 



t Cells transferred to other bath. 



52 Bulletin of the Bureau of Standards, ivoi. 4, no. i. 

TABLE Vni. 
Clark Cells — Electrolj^c Mercurous Sulphate made with old Apparatus: 
[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Date 


Mercu- 
roua sul- 
phate 


Zn804 


Zn 
Amalg. 


•** 


^r May 

1 


June 
ao 


July 
ao 


Aug. 

4 


57 


Hov. 20, '06 
tt 

tt 
Apr. 12, '06 
HOT. 23, '06 
Hov. 20, '06 
Apr. 12, '06 
IfOV. 20, '06 

tt 

Apr. 12, '06 
IfOV. 23, '06 

WOV. 20, '06 


*7 
*7 

a« 
ag 
*'« 
a« 
a« 

«10 

*'io 
All 
*'ll 

«u 
an 






+46 
+34 
+38 
+34 

+27 
+20 

+15 
+31 

+44 

+11 

+25 
+ 5 
+ 4 
+10 

+ 2 












58 










59 










60 




1 


1 


42 
42a 


+1 


-6 


+12 


+5 


-17 


61 












43 
62 


+41 


+39 


+46 


+38 


+37 


63 












44 
44a 


-2 


+1 


-6 


-18 


-14 


64 












65 












66 




1 






67 




1 






68 










69 



















Cells 57, 58, 60, 42, 62, 63, 67, 68, 69 found cracked and layer of zinc sulphate 
lifted. Replaced in bath after crystals were shaken back. 

TABLE IX. 

Clark Cells — Electrolj^c Mercurous Sulphate made with New Apparatus. 

Concentration of Sulphuric Acid exceeding Gram-Molecular, 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Date 


Mer- 
curous 
sul- 
phate 


ZnS04 


Zn 
amalg. 


• 


«>* 


♦♦♦ 


May 

I, 
Z906 

+ 5 



""^^ 


June 
ao 


July 
20 


?7h 


Apr. 12, '06 
tt 

Wot. 23, '06 
Apr. 12, '06 
W07. 23, '06 
June 28, '07 
Apr. 12, '06 
WOV. 23, '06 


bi 
Ih 
Ih 
b« 

ba 

b. 
b. 










- 1 

- 1 


+ 5 
- 2 


+ 5 



?7h 








27c 




+20 


+ 8 


28 


+ 4 


+ 2 


- 3 


- 2 


28a 


+22 


+13 
+21 


+ 1 
+ 9 


78b 










29 


- 1 








29a 




+ 13 


+ 7 









JfS'^^J Clark and Weston Standard Cells, 53 

TABLE VIII. 

Clark Cells — Electrol3^c Mercurous Sulphate made with old Apparatus. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Sept. 13 


Oct. 13 


Nov. a 


Nov. 19 


Dec. z 


Jan. xo, 

1907 


Mar. z 


Mar. a6 


May 24 


July 33. 


X 57 


1 






+41 
+31 
+33 
+29 


+20 

+14 
+28 
+15 
+10 
+14 
+13 
+30 
- 7 
+ 5 


+ 2 +8 
-21 +12 
+32 +33 
+19 +20 
-10 - 3 
+21 +20 
+19 +19 
+34 +32 


-21 


A- fi 


58 

59 


1 






broken 


! 


1 


+30 4.30 


60 




! 


+20 
-10 
+19 
+20 
+31 


+20 


42 




1 


-13 


42a 




i 


+21 
+18 
+28 
+14 
+28 


+17 


61 


1 1 


+18 


43 

62 


+37 +35 


+35 


+34 


+26 


63 


1 






+ 19 1 +12 
broken 

+33 ! 4-33 


+ 5 


+21 


44 


-10 1 -8 


—11 


-, 




44a 

64 
65 
66 

67 
68 
69 


1 




+42 

+10 
+24 
+ 3 
+ 1 
+ 5 



f29 

+ 2 
+15 
+ 1 
- 5 
- 7 
-22 


+32 

+ 6 
+18 

+ 7 
+ 7 


+29 






1 


+ 6 
+17 
+ 5 
+ 6 
- 3 
-18 


+ 7 
+18 
+ 5 
+ 7 
- 1 
-20 


+ 6 






1 


+ 4 






1 


+ 7 




1 


4-12 




1 


broken 




::::::::::i::::;::j:::::::;: 


broken 


1 1 1 







Cells 57, 58, 60, 42, 62, 63, 67, 68, 69 found cracked and layer of zinc sulphate 
lifted. Replaced in bath after crystals were shaken back. 

TABLE IX. 

Clark Cells — Electrolytic Mercurous Sulphate made with New Apparatus. 

Concentration of Sulphuric Acid exceeding Gram-Molecular. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Aug. 

4 


! 

Sept. - Oct. 
13 1 13 


Nov. 

a 


Nov. 
19 


Dec. 

z 


Jan. 
10, 
1907 


Mar. 

z 


Mar. 
216 


May ! July 
94 34 


27a 
27b 
27c 
28 

28a 
28b 


+ 4 


+ 4 1 + 4 
Broken 


+ 4 


+ 5 


+ 5 


+ 4 


+ 4 


+ 5 


+ 7 +4 








+ 6 

- 4 

- 1 


+ 6 
- 6 

+ 1 


+ 6 
- 7 

+ 1 


+ 6 
- 7 
+ 1 


+ 7 
- 4 


+90^ 


~ 4 


- 5 


- 6 


- 5 


- 4 


- 5 














+10 


29 
























29a 










! +5 


+ 2 


+ 3 


+ 3 


+ 8 


+ 2 



54 



Bulletin of the Bureau of Standards, 
TABLE IX— Continued. 



\_VoU4,No,x. 



Cell 



Date 



Mer- 

curoua 
■ul- 
phate 



ZnS04 



Zn 
amalg, 



May 

z, 
Z906 



May 

a8 



June 

ao 



July 

90 



73 
74 
75 

30 

30a 

301> 

31 

31a 

31b 

31C 

31d 

32 

32a 

32b 

33 

33a 

34 

34a 

34b 

35 

36a 

36b 
36c 

37 
38 
39 

3da 

39b 

40 
41 
70 

71 

7la 

71b 

111 



Hot. 8S, '06 



Apr. 12, '06 
Hov. 23, '06 



Apr. 
Wov. 
Ifov. 
Ifov. 

Apr. 
Hov. 



12, '06 
27, '06 
23, '06 
27, '06 

12, '06 
23, '06 



June 28, '07 

Apr. 12, '06 

Wov. 23, '06 

Apr. 12, '06 

Wov. 23, '06 

June 25, '07 

Apr. 12, '06 

Nov^. 23, '06 

Dec. 3, '06 



Apr. 12, '06 



HOT. 23, '06 
June 25, '07 

Apr. 11, '06 



W07. 20, »06 



Dee. 3, '06 



June 28, '07 



b* 

b6 

be 

br 
br 
l>r 
b« 
bg 
b| 
be 
b« 
b» 
l>. 
b» 

bio 
Iho 
bii 
bii 
Ihi 
bis 

bi, 
bi, 
bis 

bi4 
biB 
bie 
bi6 
bi6 

Htt- 
lett'il 

Hu- 
lett'sl 

Ha- 
lett'sl 

Htt- 
lett'sn 

Htt- 

lett'sn 

Hn- 
lett'sn 

Gutbe 



a 
a 
a 

b 

a 
a 
b 
a 
a 
a 
a 
b 
a 
a 

b 

a 
b 

a 
a 
b 

a 
a 
a 

b 
b 
b 

a 
a 

b 

b 

a 

a 
a 
a 



b 

a 
b 
b 

a 

b 
b 
b 

a 
a 
a 
b 
b 

a 

a 

b 

b 
b 

b 



+ 9 





+14 



+14 



+ 7 

+22 



+ 6 



+19 
+28 
+24 



+16 
+18 



+ 6 

+ 9 



+12 



+27 
+13 



+ 7 
+20 



+ 8 
+ 8 
+ 8 



+ 7 
+ 9 



+51 



+16 
+17 

+49 



+ 7 
+17 
+ 8 



+ 9 
+19 



+ 6 

- 3 

+ 2 

+ 4 



+17 
+ 8 



+ 6 



+ 4 
+14 



+ 6 



+ 4 

+ 7 



+53 



+17 



+15 



+19 



+16 



+15 



- 6 



+ 3 



- 2 



+ 2 



+ 6 



- 5 

+ 2 



- 5 

+ 1 



+ 4 



+ 5 



+ 10 
+ 9 
-13 



+10 
+10 
-10 



+35 

+24 



+39 
+30 



+ 8 



+ 5 



Broken! 



+ 2 



+ 6 




+ 4 
-10 



+ 3 
+10 
- 5 



+30 



+32 I 



Wolff. -1 
lVaiers,\ 



Clark and Weston Standard Cells, 
TABLE IX— Continued. 



55 



1 

1 Cell 


Aug. 

4 


Sept. 
13 


°.v- 


Nov. 

a 


Nov. 
X9 


O.C. 

+ 5 
+15 
+ 6 


Jan. 

ID, 
X907 


Mar. 

z 


Mar. 
a6 


May 

a4 


July 
a4 


73 
74 
75 

30 
30A 






+ 4 , + 1 
+14 4-17 


+ 2 
+18 
+17 


Broken 












Cracked 












Cracked 


+16 


+ 14 1 +11 


- 6 


+ 1 




Bio 


ken 


1 




+ 7 

+17 


+ 5 
Given 






-84Ufted 

0inn TTniv. 


1 30b 




1 






tA #3mw0« WflAhifi 


: 31 




1 






! 1 1 


. ^U 




1 






+ 4 

- 5 

- 2 


1 


-13 I-IIOHR 
etonlliiiv. 


31b 




1 






Given to George Waabin 


31C 













-41 01 014-314-2 


31d 


1 














+ 1 


32 
32a 


+ 8 


+ 7 


+ 6 


+ 9 


+ 8 


+ 5 

+15 


+ 8 

+15 


+ 10 
+16 


+ 11 + 8 
+ 17 ! +16 

1 


+ 8 
+11 


32b 






1.. 


+ 8 


33 








! 1 




1 


33a 










+ 4 
- 6 

+ 2 


+ 3 

TO. 


4. 4 


^. 3 , jf. ^ ! + 3 


34 
34« 


+ 1 





+ 1 


- 1 


- 2 


-34 1 -34 
Given tL 


-33 1 Lifted 
> Pmf . GuthA 


^b 












, 1 


+10 


' 35 
, 3te 


+ 5 


+ 6 


+12 


+ 5 


+ 6 


+ 6 
+ 4 


+ 6 1 + 6 + 7InBnrope 
Given to Prof. Hnlett 


' 36b 












+ 3 +31 4.3i 4-41+5 


36c 














+ 3 -i- 4 


+ 4 


+ 5 


+ 7 


37 


- 1 
+ 9 

- 8 


+ 1 
+12 
- 8 



+13 
- 5 


- 1 
+13 
-7 



+13 
- 7 


Bn 

+15 
- 8 

+ 2 


)ken 






38 
39 

39a 

39b 

I40 


+21 

- 8 

Broken 


+23 
- 7 


+25 
- 7 


+25 
-3 


+23 


















+ 5 
+35 












+32 
+44- 

+53 

+15 


+30 

+35 

+54 


+34 


+35 


+35 


41 


+31 


+34 


+34 


+33 


+34 




+26 


70 


4-S3 


+58 


+57 


+59 


71 

7U 

71b 

111 













Broken 














1 
-53 Ciac 


ikAd 



















+17 +19 +19 


+ 19 


+18 












+49 




1 1 




"" 1 1 





56 



Bulletin of the Bureau of Standards. 



[ Vol. 4, A'o. /. 



TABLE X. 

Clark Cells — Electroljrtic Mercurous Sulphate made with New Apparatus. 

Concentration of Sulphuric Add, Gram-Molecular or Less, 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 1 Date 

1 


Mercurous 
sulphate 


Zn804 


Zn amalg. 


Nov. 36, 


Nov. ay 


T 
Nov. 98 


48 


lfov.,'06 


Dso 






+22 


+17 


+17 


49 




bn 






+23 


+15 


+15 


50 




t>» 






+25 


+21 


+18 


51 


bo 






+19 


+15 


+11 ■ 


52 




b« 






+23 


+22 


+17 1 


53 




b» 






+36 


+34 


+32 ' 


54 


; bii 






+13 


+17 


+ 3 


55 




b,. 






+17 


+13 


+ 8 


56 




b,9 






+26 


+23 


+20 



TABLE XL 

Clark Cells — Chemically Prepared Mercurous Sulphate. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 



Date 



Mer- 
curous 

sul- 
phate 



78 


Wov. 


23, 


»06 


C 


79 




<( 




dl 


76 




f ( 




d. 


46 


Apr. 


12, 


'06 


•i 


46a 


Dec. 


3, 


'06 


•i 


46b 




tt 




ei 


86 


Nov. 


27, 


'06 


ei 


86a 


Jun© 


28, 


'07 


ei 


87 




f 1 




«f 


88 




II 




^ 


89 




II 




•4 


90 




II 




es 


91 




II 




«. 


9U 




II 




•• 


45 


Apr. 


12, 


'06 


fi 


47 




11 




U 


84 


Hov. 


27, 


'06 


Ci 


85 




II 




& 


82 


Wov. 


27, 


'06 


hi 


83 




it 




y^ 


77 


Wov. 


23, 


'06 


b. 







Clark and Weston Standard Cells. 



57 



TABLE X. 

Clark Cells — Electrolj^c Merciirous Sulphate made with New Apparatus. 

Concentration of Sulphuric Acid, Gram-Molecular or Less. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Dec. I 


Dec. 6 


Jan. 4, 
1907 


Jan. xo 


Jan. 3X 


Mar.x 


Mar. a6 


May 34 


July 23 


48 
49 
50 

51 
52 
53 

54 
55 
56 


+15 
+13 
+15 

+14 
+20 

+34 

+ 4 
+ 8 
+17 


+15 


+11 
+13 
+ 7 

+10 
+20 
+28 

+ 2 
+ 6 


+14 
+ 4 
+15 

+22 Li 

+23 

+31 

+ 5 
+ 8 


+15 
+ 5 


+15 

— 2 


+14 
+ 5 


+15 
+ 7 


+11 
+ 8 


+16 

+14 
+21 
+30 

+ 5 

+ 8 


Ciackad 


— 5 


ttted 

+24 

+33 

I4ft6d 

+ 9 










+23 
+35 


+24 
+37 


+25 


+23 






+12 


+ 8 


+10 


+ 9 



















TABLE XI. 

Clark Cells — Chemically Prepared Mercurous Sulphate. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Aug. 

4 


Sept. 
13 




Oct. 

13 


Nov. 

3 


Nov. 
19 


Dec. 

X 


10, 
X907 


Mar. 

X 


Mar. 

36 


May 


July 

23 


78 




+ 8 

+11 
+ 6 

- 7 


+ 7 

+ 5 

- 4 

- 8 

- 8 

- 8 
-17 


+16 


4-18 


+17 


+13 


79 












CxHCksd 
+ 1 — 2 


+ 9 


76 






1 




+ 6 

- 4 

- 4 

- 4 
-12 


+29 


46 
46a 


-14 


-11 


-12 


-13 


- 8 


- 4 

- 4 

- 2 
-17 


- 4 

- 3 

- 4 
-13 


- 4 

— 4 


46b 


1 










86 


1 








— 8 


86a 
87 


1 








+ 3 


1 






1 


- 7 

- 2 

- 2 

- 7 

- 8 

- 8 

+ 9 

- 1 

+ 5 
-13 

-17 

- 3 

+ 9 


- 3 
+ 3 



- 1 

- 2 

- 3 

+13 

+ 4 

Cra. 


- 3 
+ 4 
+ 1 

- 2 

- 2 

- 2 

+14 

+ 4 

ckad 


- 2 

+ 7 
+ 2 

- 3 

- 2 

- 2 

+15 
+ 3 


_ 1 


88 









1 


+ 4 


89 
90 
91 
9ia 

45 

47 

84 
85 

82 
83 

77 








1 


+ 1 
— 3 








! 


1 




1 ! 


— 3 




: 1 1 


+ 1 

+13 
- 1 


+ 8 

+ 1 


+11 

+ 1 


+ 9 
- 1 


+ 8 
+ 1 


+11 

+ 1 


+ 8 

- 1 

+17 
+17 

-13 

+ 6 
+10 












— 3 — 2 




+ 5 












-13 
+ 3 
+11 


-13 

+ 2 
+11 


-13 
+ 2 

+12 


—11 












+ 2 
+11 























58 



Bulletin of the Bureau of Standards, 
TABLE XII. 



\VoL4'No.i, 



Clark Cells. — Specially Treated Commercial Samples of Mercuious 

Sulphate. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Date 


Mer- 

curoua 
■ul- 
pbate 


Zn804 


Zn 
Amalg. 


* 


«* 


•** 


May 

z, 
Z906 


May 
38 


June 
ao 


July 

ao 


80 


Ifov. 27, '06 
tt 

April 11, '06 

tt 

tt 
Nov. 23, '06 
April 11, '06 
KOV. 27, '06 
April 11, '06 
JXOV. 23, '06 
April 11, '06 

VOV. 27, '06 
tt 
tt 
It 
It 

April 11, '06 
tt 

Vav. 27, '06 
April 11, '06 
Vov. 23, '06 
April 11, '06 

tt 

tt 


ll 
U 

ki 
k. 
ks 
ks 
k4 
k4 
k6 
k6 
k, 

ll 
h 
h 
U 

l6 

ni 
n< 
n« 
ns 
n« 
^ 

n« 






+10 

+ 3 


+ 3 
- 2 


+ 1 
- 3 






1 


81 








21 


+ 2 

+ 23 

+ 55 

+ rs 


+ 2 
+ 25 
+ 50 

-1- 27 


- 6 
+ 15 
^ 56 


- 3 

+ 17 
4- 51 


22 


1 




23 


1 




23a 




+29 


■ " 1 


24 


1 


+ 19 


+ 20 


24a 


+11 


+ 9 


+ 9 






25 


+ 50 


+ 47 


+ 47 


+ 48 • 


25a 






+26 




26 






+ 16 


+ 17 


+ 29 


+ 20 


92 


+28 
+57 
+25 
+71 
+47 


+26 
+57 
+25 
+77 

+52 


+29 

+61 
+ 20 
+77 

+52 


93 










94 




...J 1 


95 










96 










15 


+ 59 
+112 


+ 65 
+121 


+ 55 

+111 


+ 61 
+115 


16 








16a 


+76 


+77 


+78 


17 


+143 


+147 


Broken 
1 


17a 






+76 


18 






+ 74 
+162 
+ 96 


+ 71 
+157 
+ 97 


+ 59 
+145 
+ 93 


+ 62 

+146 
+ 93 


19 








20 


b A 




1 













Woiff. -I 



Clark and Weston Standard Cells. 
TABLE XII. 



59 



Clark Cells — Specially Treated Commercial Samples of Mercurous 

Stilphate. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Aug. 

4 


Sept. 
13 


Oct. 
X3 


Nov. 

a 


Nov. 
19 


Dec. 

X 


Jan. 

10, 

1907 


Mar. 

z 


Mar. 

a6 


May 


July 
23 


80 




' 




+ 1 

- 4 

- 4 
+ 25 
+ 46 
+ 30 


- 7 

- 8 

+ 2 
+ 28 
+ 49 
4. 31 


- 3 

- 3 

+ 2 
+ 33 
+ 52 
+ 35 


- 2 

- 3 

+ 1 
+35 
+53 


- 1 

- 1 

- 1 
+ 28 
+ 55 
+ 36 


- 6 


81 


::;:::::::::::!:::::::: 






- 3 


21 
22 
23 
23a 



+ 17 
+ 48 



+ 21 
+ 49 


- 2 
+ 24 
+ 53 


- 4 
+ 25 
+ 48 


- 4 
+ 23 
+ 49 


- 5 

+12 
+52 
+37 


24 
! 24« 

1 " 

2Sa 

26 

1 92 
1 93 


+ 17 


+ 19 


+ 18 


+ 17 


+ 14 


Broten 

+ 7 4-6 






+ 2 
+ 58 

+ 30 

+ 24 

+ 24 
+ 63 




- 2 

+59 
+33 
+24 

+28 

•4-60 



+ 58 

+ 32 
+ 22 

+ 22 
+ 60 


fl4 


+ 46 


+ 49 


+ 50 


+ 48 


+ 53 


+ 52 

+ 25 
+ 16 

+ 24 
+ 55 
+ 23 
+ 75 
+ 50 

+ 51 
Bit 


+ 56 
+ 26 
+ 20 

+ 20 
+ 57 

- 1 
+ 67 
+ 42 

+ 42 


+45 
+29 


+ 20 


+ 17 


+ 20 


+ 18 


+ 19 


+ 16 

+ 9 


, 




+59 


94 
95 


' 






Broken 

+ 73 1 +71 




1 






+ 72 


-t-73 


96 


] 






+ 41 

+ 35 


+43 
+39 


Broken 


15 
16 


+ 60 
+121 


+ 60 
+114 


+ 57 
+114 


+ 56 

+118 


+ 60 
+118 


+ 33 


+29 


16a 






+ 75 1 -4-75 


+ 81 


+81 


+ 79 


+79 


17 
















17a 








+ 74 
+ 67 
+150 
+ 92 


+ 67 
+ 68 
+141 
+ 93 


Clacked 






18 
19 
20 


+ 66 +65 
+149 +146 

+ 94 +93 

1 


+ 64 
+146 

+ 93 


+ 63 
+152 
+ 94 


+ 67 
+150 
+ 95 


+ 73 
+142 
+ 99 


+72 
+89 
+98 


+ 68 
Cracked 
+100 


+65 

I +85 

+99 



6o Bulletin of the Bureau of Standards. \yoi.4.No.t. 

TABLE Xin. 

Clark Cells. — Set up with Commercial Samples of Mercurous Sulphate 

according to Old Specifications. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cell 


Date 


Mercurous 
Sulphate 


Zn804 


Zn 
Amalg. 


May 
z, zgo6 


"^'^ 


June 

90 


July 

ao 


Aug. 

4 




April 9, '06 


KaUbaumA 






+ 387 


+ 353 


+ 327 


+ 320 


+ 319 




<i 


i< 






+ 442 


+ 379 


+ 378 


+ 366 


+ 366 




(1 


<f 






+ 442 


+ 375 


+ 372 


+ 362 


+ 360 


10 


(< 


KaUbanmB 






+ 526 


+ 489 


+ 487 


+ 489 


+ 482 


14 


Aprilll, '06 


ITaMhmitw C 






+ 305 


+ 245 


+ 241 


+ 221 


+ 212 




April 9, '06 


<< 






+ 404 


+ 302 


+ 295 


+ 272 


+ 265 




<< 


Merak 






+ 282 


+ 248 


+ 248 


+ 244 


+ 249 


12 


*' 


Sdiiiduudt 






+2202 


+1652 


+1587 


+1366 


+1275 


13 


(< 


(< 






+2172 


+1646 


+1585 


+1350 


+1241 


' 


<i 


Gehe 






+ 412 


+ 377 


+ 376 


+ 373 


+ 376 




f ( 


K 






+ 422 


+ 381 


+ 383 


+ 377 


+ 379 



TABLE XIV. 

Ebcchange Cells. 

[Differences in Microvolts from Mean of Reference Cells.] 



WESTON CELLS. 



Cell 




Date 


Mercurous 
Sulphate 


CdS04 


Cd Amalg. 


July 
X906 


July 
so 


F7 
04 


Hntott 

Hnlett 


Feb. 15, '04 


l:6H^4D».25.... 


Kahl.reciys- 
talised 


12i)(C.P.Merok 




- 62 


05 


Hnlett 














A3 

A52 

1 


Hnlett 

Hnlett 

Hat.Phy.Lab. 
Hat.Phy.Lab. 
Guthe 


Oct. 21, '05 

July, '06 

Feb., '06 
Feb., '06 


l:6HgS04D».82 .... 
l:6H^S04]>».35.... 
Fuming Sulphuric. 


talized 
talized 


121 )( C.P.Merck 
12i)( C.P.Merck 
9;tCd 


-80 
-85 


+ 48 

+ 34 

- 78 
-104 


2 




9)(Cd 


Cl 




Merck and 
Baker, ra- 
crystalized 


12|)fK«hl 


5 


Cariiait 

Caihait. ...... 

W.W.Strang. 
W.W.Strang. 
W.W.Strang. 


July 21, '06 
July 25, '06 

June 15, '07 
June 15, '07 
June 15, '07 


m. l:9H^S04 








8 


El. 1:9H|S04 










1 


b29 
b29 
b29 




I'.l 4KAhl. FI, . 






2 










3 



















*rS'/^j.] Clark and Weston Standard Cells, 6i 

TABLE XIII. 

Clark Cells. — Set up with Commercial Samples of Merctirous Sulphate 
according to Old Specifications. 

[Differences in Microvolts from Mean of Reference Cells.] 



Cril 



Sept. 
13 



1 
2 
3 
10 
14 
6 
5 
12 
13 
8 
9 



+ 307 
+ 359 
+ 351 
+ 473 
+ 190 
+ 246 
+ 241 
+1066 
+ 977 
+ 369 
+ 373 



Oct. 

13 



+307 
+357 
+352 
+474 
+181 
+237 
+242 
+937 
+790 
+371 
+378 



Nov. 

a 



Nov. 
19 



+303 
+352 
+347 
+470 
+178 
+240 
+230 
+854 
+669 
+370 
+377 



+300 
+355 
+349 
+472 
+177 
+226 
+240 
+790 



Dec. 

z 



+297 
+351 
+348 
+470 
+172 
+219 
+239 
+745 



Clacked 
+369 +367 



+379 



Jan. 
zo, 1907 



+297 
+256 
+348 
+473 
+172 
+214 
+240 
+598 



+371 



Broken 



Mar. 



+294 
+334 
+350 
+474 
+172 
+203 
+239 
+414 



Mar. 
36 



+373 



+290 
+328 

+344 
+468 
+163 
+194 
+233 
+322 



May 
a4 


July 

23 


+287 


+267 


+344 


+311 


+326 


+328 


+473 


+461 


+158 


+142 


+187 


+170 


+230 


+217 



+368 i +372 



+180 Cracked 
+ 27 

+364 



TABLE XIV. 

Exchange Cells. 

[Differences in Microvolts from Mean of Reference Cells.] 

WESTON CELLS. 



Cell 


Aug. 

4 


Aug. 
ax 


Sept. 
13 


Oct. 

13 


Nov. 

9 


Nov. 
19 


Dec. 

z 


Jan. 
zo, 
Z907 


Mar. 

z 


Mar. 
95 


Apr. 
a4 


May 

24 


June 
a6 


July 
33 


P7 


-67 


-80 


- 88 


- 96 


-118 


-121 


-126 


-150 


-227 


-306 


-375 


-417 


-466 


-500 


04 


+47 


+47 


+ 47 


+ 47 


+ 49 


+ 50 


+ 45 


+ 50 


+ 46 


+ 47 


+ 46 


+ 49 


+ 51 


+ 51 


05 


+ 17 


+25 


+ 26 


+ 35 


- 23 


- 21 


+ 8 


- 43 


- 25 





+ 6 


- 17 


-119 


-956 


A3 


+46 


+48 


+ 47 


+ 49 


+ 49 


+ 50 


+ 47 


+ 52 


+ 48 


+ 48 


+ 47 


+ 44 


+ 41 


+ 42 


AS2 


+30 


+30 


+ 27 


+ 28 


+ 30 


+ 32 


+ 32 


+ 29 


+ 29 


+ 30 


+ 29 


+ 29" 


+ 28 


+ 29 


1 
2 


-78 
-98 


-91 
-99 


- 95 
-107 


-107 
-111 


-113 
-126 






-130 
-128 


-165 
-112 


-173 
-129 


-186 
- 96 


-208 
-125 


-226 
-122 


-242 




-112 


-107 


01 
















+ 26 


+ 25 


+ 23 


+ 22 


+ 17 


+ 18 


+ 16 


5 
8 

1 
2 

3 
















+ 4 
+ 12 



+ 11 



+ 13 


- 1 
+ 9 



+ 10 


- 3 

+ 9 


— 3 
















+ 7 


















June 
aa 


June 

24 


June 
a6 


June 
99 


July 
zo 


July 

33 


+38 
+53 
+10 


+29 

+41 
-15 


+27 
+36 
-16 


+20 
+30 
-16 


+ 8 
+14 
-17 


+ 1 


















+ 6 



















-23 














1 ' ' 





8919—07 5 



62 



Bulletin of the Bureau of Standards, 
TABLE XIV— Continued. 

CLARK CELLS. 



\Vol.4.T^'o.i. 



Cell 



Date 



Mercurous 
Sulphate 



I 



ZnS04 



Zn Amalg. 



July 
X906 



Aug. 

4 ; 



H4 

H18 

bl 

C2 



Hulett.. 
Hulett.. 
Guthe... 
Carluut . 



Mar. 15, '04 
Feb. 25/06 



l:6HtS04D».25...'Scli.twioexe- 10 i C. P. 

cnrstalized Baker 
l:6BsS04D».82... Bl.AtwJceie-l 10 i C. P. 
cryetalixed 1 Baker 

Hulett ' C.P.Sch.re- 10 jf 

I cryetalixed \ 
Vw. 14/06 j Bl.l:6HaS04 : 



-9 

+6 



I 



TABLE XV. 

Weston Cells. 

{Set up by Mr. P. I. Wold.) 

[Differences in Microvolts from Mean of Reference Cells.] 
X906 



Cell 


Date 


Hb,804 


CdSOf 


Cd Hot 

Amalg. "«f- 


June June 

30, 90. 

a.m. p. m. 


July 
3 


20 
27 


June 8, *06 
n 


1:6 H^4 
D=.3Anip. 




>Ji^U^ 2 


-19 
+10 


-11 
+16 


-23 
-10 


21 


n 


(< 


(C 


|| 


- 5 


- 2 


-18 


24 


tt 


<< 


It 







+ 6 


-11 



X907 



Cell 


Date 


Hg,S04 


Cd804 


Cd 
Amalg. 


Hg. 


June 
14 


June 


June 


42 


April, >07 


l:6Ht804D=.3 


Reciystallsed 


ByElectr. 




- 7 


- 9 


- 9 


46 




" D=l 




i< It 


s 


+ 2 





+ 1 


49 




" D=l 




Melted 


§ 


-25 


-21 


-22 


50 




'* D=l 




It 


3 


+14 


+13 


+13 


55 




Hulett'8 




ByElectr. 


s 


-17 


-17 


-15 


57 




l:6Ht804D».4 




It It 


► 


-52 


-53 


-58 



lVaUrs.\ 



Clark and Weston Standard Cells. 
TABLE XIV— Continued. 



63 



CLARK CELLS. 



Cell 


Sept. 
13 


Oct. 
13 


Nov. 

3 

- 7 


Nov. 
»9 


Dec 

I 


Jan. 
xo, 
1907 


Mar. 

X 




Mar. 

36 

- 3 


May 

a4 

- 1 


July 
33 


H4 


- 8 


- 5 




+ 1 




m. 


+14 


+16 


+13 


+18 


+15 


+22 


+25 


+30 


+22 


+21 


M 












+71 


+58 


+65 


+63 




C2 











+14 


+44 


- 8 


-18 

















TABLE XV. 

Weston Cells. 

(Set up by Mr. P. I, Wold.) 

[Differences in Microvolts from Mean of Reference Cells.] 
X906 



Cell 


1 

July j July 
5. a.m. 5. p.m. 


1 

July 1 July 

6 9 


July 

XX 


July 

30 


July 
•4 


Aug. 

4 


Aug. 
17 


Sept. 

XX 


Sept. 
X3 


! 2. 

\ 27 
I 21 


-16 -11 -12 -13 

-41+4 - 1 1 _ 3 
-17 


-12 
- 2 


-17 
-13 


-11 -23 
- 8 -14 


-12 
-17 


- 6 ; -15 

- 9 ' -11 


i U 


-9 ' 1 ' 












i 


1 










i 



X907 



Cell 

42 
46 
49 
50 
55 
57 



June ' June 1 June June { June I June 

X7 I x8 X9 



- 7 
+ 5 
-18 
+13 
-15 
-58 



-10 


- 9 


- 9 


+ 1 





+ 2 


-20 


-19 


-19 


+16 


+15 


+16 


-16 


-16 


-16 


-61 


-60 


-61 



June 



- 9 I -12 
+ 3 I + I 
-20 I -22 I 
+16 I +15 
-16 -16 I 
-64-65 



- 9 
+ 4 
-19 
+18 
-14 
-62 



- 9 
+ 2 
-19 
+-17 
-15 
-59 



June 
39 


July 

xo 


July 
33 


—11 






+ 1 






—14 






+18 






-12 






-53 


-68 


-69 



64 Btilletin of the Bureau of Standards, \voi. 4. no. /. 

DISCUSSION OF RESULTS. 

Weston cells, — An inspection of the figures given in Tables III 
to VII shows that there is a highly satisfactory agreement between 
cells made with all the samples of mercurous sulphate prepared by 
methods a to k^ inclusive, with the exception of a few of the white 
samples prepared in 1904, of which only scant quantities were pre- 
served. In addition, two of these, a^ and «,> were somewhat discol- 
ored, probably by the action of light. 

In cells Nos. 26 to 44, inclusive, the first Weston cells set up in 
1906, the platinum terminals inside the cell were not amalgamated. 
Perhaps for this reason the agreement was not as close as could 
have been wished, as duplicates with amalgamated terminals showed 
a much smaller deviation from the mean. In general the cells with 
abnormally high initial values, with the exception of those in Table 
VII, have shown a decided decrease, in a few cases dropping below 
the normal value. Cells 9 and 42 showed a sudden decrease in 
value, but in each case they were found to have cracked. 

The most satisfactory results, on the whole, were obtained with 
cells in which gray samples of electrolytic sulphate were employed, 
as shown in Table IV. A comparison of the values on July 20, 
1906, and July 23, 1907, shows an average decrease of 6 microvolts 
for the interval. (Table XVII.) 

Even with the samples of electrolytic mercurous sulphate pre- 
pared with more dilute sulphuric acid (F=i, 2, and 5), Table V, 
the agreement is very good and with the exception of No. 59, which 
had the highest initial value, the average relative change within 
the above-mentioned interval being 13 microvolts. 

The agreement of the cells in Table VI, in which chemically 
prepared sulphate was used, compared with those made with elec- 
trolytic sulphate, is excellent ; relatively large changes are shown, 
however, by the three samples made by reduction of mercuric 
sulphate by sulphurous acid, which gave abnormally high initial 
values, and by cell 107. 

From Table VII it may be seen that commercial satpples of mer- 
curous sulphate, when digested with sulphuric acid, no longer show 
the large initial changes ordinarily observed when this treatment is 
omitted, and that digestion with hot 1:4 sulphuric acid, series z and k^ 



2^2^^^ ] Clark and Weston Standard Cells. 65 

brings the commercial samples into excellent agreement with those 
prepared electrolytically. With few exceptions, the relative changes 
are ver}' small. Most of the samples of series /, m^ and n^ which 
were prepared by allowing commercial mercurous sulphate to stand 
for a long time in contact with sulphuric acid, gave slightly high 
initial values which have persisted, in marked contrast with the 
usual behavior in such cases. 

Clark cells, — ^The agreement of the Clark cells is on the whole 
somewhat better than that of the Weston cells, though, on account 
of their tendency to crack and the fact that many of them were not 
set up until November, 1906, the tables are less complete than in 
the case of the Weston cells. Although some of the Clark cells are 
more than a year old, the formation of gas at the amalgam limb, so 
frequently mentioned, has not been observed in cells which cracked 
in the bath, and which, therefore, were completely immersed in the 
kerosene. In such cases the development of a crack was generally 
followed by infinite resistance owing to the penetration of kerosene 
into the cell, in consequence of the slightly diminished pressure 
produced in sealing. As shown in the tables the cells resumed their 
normal values on cautiously shaking down the crystals which had 
been lifted by the layer of kerosene. In cases where the crack was 
so large as to expose the amalgam the electromotive force rapidly 
decreased. 

Tables VIII to XII give the results obtained in the same order as 
in Tables III to VII. The deviations from the mean for the same 
ssftnple of mercurous sulphate will, in general, be found to agree 
closely for both types of cell. 

Table XIII gives the measurements on Clark cells set up with 
six untreated commercial samples of mercurous sulphate in accord- 
ance with the old specifications, in which the zinc sulphate solution 
was treated with an excess of zinc oxide, then with mercurous sul- 
phate and filtered, while the latter was washed with water. These 
cells were set up in April, 1906, and had very high initial values 
in May, when first measured, and after the lapse of a year are, on 
the average, 280 microvolts above the mean. 

Exchange cells. — During the progress of the work Clark and 
Weston cells were exchanged with Professors Hulett, Carhart, and 
Guthe, and in June, 1906, two Weston cells were kindly sent us by 



66 Bulletin of the Bureau of Standards. [loi. ^, .vo. i. 

the National Physical Laboratoty of England. These have been 
kept under continuous observation, and the results obtained are 
given in Table XIV. This table also gives the measurements on 
three Weston cells set up by Mr. W. W. Strong at the Johns Hop- 
kins University with mercurous sulphate, mercury, and cadmium 
furnished by the Bureau, the cadmium sulphate being purified by 
him." 

In July, 1906, a number of Weston cells set up by Mr. P. I. Wold, 
of Cornell University, were measured at the Bureau ; the results 
obtained on these and also on others received in June, 1907, are 
given in Table XV. Further data on these and the exchange cells, 
kindly placed at our disposal by Professors Carhart, Hulett, and 
Guthe, and by Mr. Wold, are given in the tables. 

Professor Hulett's cells, with the exception of B\ and Oj, have not 
appreciably changed with respect to our cells during the period in 
which they have been under observation. Both of these cells, as 
well as O4, have defective seals which have allowed the penetration 
of oil. The paste of 7^ is quite brownish and the amalgams of Fj 
and O5 are slightly coated with a black deposit, possibly finely 
divided mercury. In addition, the values of O^ show irregular 
changes. 

The agreement of the cells of Guthe and von Ende** with the 
Bureau's cells indicates that the Clark cells obtained by them from 
Professor Hulett, constructed in 1904 and used as their basis of ref- 
erence, must have suffered some change, possibly due to " exposure 
for some weeks to diffused light." Although Guthe and von Ende 
found relatively large initial changes in the electromotive force of 
their Weston cells, the measurements made at the Bureau on one of 
them showed that it had reached a practically constant value in close 
agreement with the Bureau cells when received. 

The results obtained with the exchange cells, with the exception 
of cells /^7 and O^ and the two cells from the National Physical 
Laboratory of England, which also contain oil, show that cells set 
up by different observers are in satisfactorily close agreement. This 
is also shown by the cells set up at the Bureau with samples of 

"Three abnormally low Clark cells, two probably inverted, were also received 
from Mr. Strong. 
**Phys. Rev., 24, p. 214 (1907). 



H'olff. 1 
WaUrs J 



Clark and Weston Standard Cells, 



67 



mercurous sulphate obtained from Professors Hulett and Guthe. 
(Tables IV and IX.) 

TABLE XVI. 

Values of Weston Cells in Terms of Clark Cells.' 



Date 


Diff. method Direct method ' 


Date 


Diff. method 


Direct method 


Jnne 1, '06 
Jnne 2 
Jnne 4 
Jnne 7 
Jnne 9 
Jnnell 
Jnne 13 


1.018859 


1 


Sept. 13, '06 
Sept. 21 
Oct. 13 
Nov. 3 
Nov. 6 
Nov. 17 
Nov. 19,A.M. 
Nov. 19,P.H. 
Nov. 24 
Dec. 8 
Mar. 2, '07 
Mar. 27 
May 29 
July 26 
Jnly 29 
Jnly 30 
Blean 


1.018892 
72 
77 
70 
74 
68 
66 
69 
79 
79 
70 
64 
69 
68 
59 
69 
1.018869 


1.018890 


65 
58 
65 
51 
66 
62 


' 


81 


1.018854 
66 
59 
67 
65 
63 
64 
64 
63 
82 
88 
80 
81 
99 


70 
74 
77 
76 


JnnelS 
Jnne 19 
Jnne 20 
Jnne 22 
Jnly 14 
Jnly 20 
Jnly 24 
Jnly 26 
Anc.21 




61 
63 
61 
78 

73 
76 
84 




83 
73 


68 
72 




1.018873 



'Weston cells i, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, and 15. Clark cells 27a, 28, 32, 34, 
and 39. 

Relative values of Weston and Clark cells, — Table XVI shows 
the values of the mean of the twelve Weston cells, taken as the 
basis of reference, in terms of five Clark cells similarly used. The 
measurements were made by the direct and differential methods. 
In the former, the five Clark cells and seven of the twelve Weston 
cells were separately measured, and in the latter the cells of each 
set were arranged in series and the difference obtained by placing 
the sets in opposition. In the computations the value of the mean 
of the Clark cells was taken as 1.42110 volts at 25°, derived from 
the value, 1.434 volts at 15°," adopted by the Chicago Congress for 
the Clark cell set up in accordance with the old specifications. A 
correction of —0.00030 volt was made for the average difference in 
electromotive force obtained with the specially prepared mercurous 
sulphate. 

On account of breakage the same five Clark cells were not 
employed throughout the whole period, but the results were reduced 



"^i=^,4-.ooii9 (/-15) -.000007 (^-15)' 



68 Bulletin of the Bureau of Standards. [Voi. 4, -^'o. j, 

to the mean of the five which lasted longest. The new cells sub- 
stituted for the broken ones agreed closely with the latter, so that 
the necessary corrections in no case exceeded five microvolts. 

The close agreement between the results obtained by the direct 
and differential methods indicates that errors incident to electrical 
measurements are practically eliminated. The values obtained on 
the dates given can therefore be affected only by errors in temper- 
ature measurement (o.oi ° = 9 microvolts), by possible hysteresis due 
to occasional interruptions in the regulation of the baths, and to 
possible ageing. The variations observed are, with two or three 
exceptions, so slight that they can be accounted for by an error of 
dbo.oi® in reading the temperature. It may, therefore, be safely 
concluded that the Weston cells in terms of which the results are 
expressed have not changed with reference to the Clark cells, dur- 
ing the fourteen months, by as much as 20 microvolts. This con- 
clusion is also confirmed, as shown in the tables, by the close 
agreement of cells set up at different times with the same sample of 
mercurous sulphate. 

SUMMARY OF RSSULTS. 

For ready comparison of the results obtained with both Weston 
and Clark cells with mercurous sulphate made by the different 
methods. Tables XVII and XVIII are given. These show the 
mean differences and the average deviations in microvolts from the 
mean of the reference cells for each set of samples. Only those 
cells are included which were under continuous observation for the 
whole period, with the exception of exchange cells and those set up 
with mercurous sulphate obtained from Professors Hulett and 
Guthe. The last column in each table gives the relative changes 
from the beginning to the end of the period covered, which, in the 
case of the Clark cells is only eight months, as most of them were 
set up in November, 1906. The number of Clark cells was also 
smaller on account of the breakage. 

The largest change for the Weston cells, as shown in Table XVII, 
is found with the white samples of mercurous sulphate prepared in 
the old apparatus, and is no doubt partly to be accounted for by the 
somewhat high initial values of some of them, as in practically all 
the other cases where a slight decrease is also shown. Part of the 



IVolff. 1 
U^atersX 



Clark and Weston Standard Cells. 



69 



decrease may be due to the gradual leaching out of traces of sul- 
phuric acid obstinately retained by the irregularly pitted crystals of 
mercurous sulphate. Although these changes are relative, an in- 

TABLE XVII. 

Summary of Results. 

Weston Cells — Mean Differences and Average Deviations, in Microvolts, for 
Each Series of Mercurous Sulphate Samples. 











July flo, '06 


October 
13. '06 


January 
xo, '07 


April a4. 
•07 


July 93. '07 


a 




Method 


■ 

f 

i 



^ 




















Table 


Is 




lg 




i 




1 

Is 




Qg 






0' 


1 


V 

> 


i 


> 


1 


r 


1 


e 


1 


f 


-8 






z 


& 


s 


< 


s 


< 


s 


< 


s 


< 


s 


< 


Q( 


m 




14 


15 


+28 


31 


+20 


24 


+10 


17 


+ 4 


16 


- 1 


16 


-29 


IV 




17 


28 


+ 3 


11 


+ 1 


10 





10 


- 1 


10 


- 3 


10 


- 6 


V 






10 


+12 


14 


+ 6 


10 


+ 1 


7 


+ 2 


11 


- 1 


12 


-13 










+ 3 


3 


+ 4 


4 


- 2 


2 


- 7 


7 


- 9 


9 


-12 










- 5 


14 


-12 


12 


-12 


12 


-30 


30 


-31 


31 


-26 


VI : 








-11 


11 


-12 


12 


-11 


11 


-15 


15 


-18 


18 


- 7 








- 9 


9 


- 8 


8 


-6 


6 


-10 


10 


-14 


14 


- 5 










+18 


29 


+ 7 


22 


+ 8 


22 


+ 6 


19 


+ 1 


16 


-17 










-10 


12 


-15 


15 


-16 


16 


-19 


19 


-22 


22 


-12 










+ 5 


7 


+ 2 


4 





6 


- 8 


8 


-11 


11 


-16 










+ 5 


11 


+ 5 


12 


+ 9 


14 


+ 5 


13 


- 2 


14 


- 7 


vn 








+32 


32 


+36 


36 


+35 


35 


+30 


30 


+14 


29 


-18 










+52 


52 


+60 


60 


+57 


57 


+52 


52 


+46' 


' 46 


- 6 










+74 


74 


+73 


73 


+77 


77 


+73 


73 


+67 


67 


- 7 



EXCHANGE SAMPLES. 



IV 


'(Hatott I 

JHnlflttn 

joatlie 


..' 1 

• ■! 1 
.. 1 


2 +32 
2 


32 


+32] 


32 


1+36 
1 ^ 


36 

4 


+36 
- 3 


36 
3 


+33 


33 


+ 1 




1 








+25 


25 

























BXCHANQB CELLS. 



XIV 
XV 



Hnlfltt.... 
Gttthe.... 
Gutart... 
W(dd, '06. 
Wold, >07. 
Straoc. ... 



-15 



+40 40 



15 



*June 14, '07. 



+44 

4 

+ 6 



+41 
- 1 

+ 4 



.,»- 14 



20 



+41 
- 3 

+ 2 



*June 29, '07. 



+ 1 

- 7 

- 4 



JO 



Bulletin of the Bureau of Standards, 



[Vol. 4. No. I. 



spection of Table XVI will show that practically no change has taken 
place in the twelve Weston cells, chosen as standards, with reference 
to the corresponding Clark cells. This is also shown by the close 
agreement of duplicate Weston and Clark cells set up from time to 
time. (Tables III to XII.) One lot of the former, particularly those 
in Table III, set up June 28, 1907, show relatively large initial values, 

TABLE XVIII. 
Summary of Results. 

Clark Cells — Mean Differences and Average Deviations, in Microvolts, for Each 
Series of Mercurous Sulphate Samples, 











Dec. ] 


.'06 


March 


1, '07 


May 34, '07 


July 34, '07 


a 




Method 


S 

a 

1 

d 

Z 


2 

d 

z 

12 




\ 














&2 


Table 


s 


s 

s 


i 

< 


s 


1 

S. 

Q 

."5 

1 


s 


1 
Q 

f 


8s 

.c 

II 


vm a 


10 


+ 23 


23 


+ 18 


18 


+ 14 


18 


+ 16 


16 


_ 7 


IX ! b 




10 


+ 4 


7 


+ 6 




+ 9 


9 


+ 6 


7 


+ 2 


X 1 b 




4 


+ 14 


14 


+ 12 


13 


+ 14 


14 


+ 13 


13 


- 1 




c 






+ 8 


8 


+ 16 


16 


+ 17 


17 


+ 13 


13 


+ 5 










+ 8 


8 


+ 5 




+ 7 


7 


+ 19 


19 


+11 














— 3 




— 2 


4 


- 2 


3 


4. 1 


XI 








+ 4 


4 


+ 8 




+ 9 


9 


+ 6 


7 


+ 2 










+ 17 


17 


- 3 








+ 5 


5 


-12 










+ 1 


10 










9 


+ 1 


8 












- 2 


2 


- 3 




- 1 


1 


- 4 


4 


- 2 


xn 








+ 24 


25 


+ 29 


29 


+ 28 


28 


+ 28 


29 


+ 4 








+ 51 


51 


+ 53 


53 


+ 51 


51 


+ 47 


47 


- 4 










+ 71 


71 


+ 72 


72 


+ 70 


70 


+ 68 


68 


- 3 


XIII Old Speciflca- 
1 dons 






+308 


308 


+305 


305 


+298 


296 


+282 


282 


-26 



EXCHANGE SAMPLES. 



IX 



xnr 



Hulettl. 
Hulettn 
Gnthe... 

Hulett.. 
Gnthe... 
Carbart. 



1 I 2 

1 I 1 

1 I 1 



+ 43 



43 



+ 44 
+ 19 



19 



+ 46 
+ 19 



46 
19 



+ 47 
+ 18 

+ 49 



47 
18 
49 



EXCHANGE CELLS. 



+ 12 
+ 58 
+ 44 



12 
58 
44 



+ 11 
+ 63 
- 18 



+ 4 
- 1 



ii'aurs] Clark and Weston Standard Cells, 71 

but at the present time are in practical agreement with those set up 
twelve months before. 

The relative changes in the Clark cells in the eight months are 
smaller than in the case of the Weston cells. Excluding those set 
up in accordance with the old specifications, the changes, which are 
both positive and negative, are less than i part in 100,000. 

Size of grain, — In view of the work of von Steinwehr on the influ- 
ence exerted upon the electromotive force by varying size of grain, 
efforts were made in some cases to obtain samples as coarse as possible, 
but the close agreement in both Clark and Weston cells of practically 
all the samples prepared by methods a to A, inclusive, shows that 
special precautions in this direction are hardly necessary. Many of 
the samples were examined under the microscope, and it was found 
that there were ver>'' few particles measuring less than one micron, the 
average dimensions being considerably greater. On the other hand, 
it is unnecessary to attempt to obtain very coarse-grained samples 
on account of the marked hysteresis, due to the small surface 
exposed to the solvent action of the electrolyte, as shown also by 
von Steinwehr. 

The irregular pitted character of the crystals of all the samples of 
mercurous sulphate, which was mentioned above (p. 28), may ex- 
plain, in part at least, the gradual decrease in the electromotive force 
of some of the cells, on account of the difficulty of completely remov- 
ing the acid in which the sample was made and preserved. 

A study has also been made of the electromotive differences of 
cadmium sulphate obtained from various makers or made directly 
from the **C. P." metal. Twenty cells, set up with clear and cloudy 
crystals, obtained by the recrystallization of 8 samples, from acid, 
neutral and basic solutions, show an average deviation from the mean 
of all of :t 9 microvolts and with a range of + 28 and — 26. 

Further work has been done on the remaining materials and on 
other factors which might influence the electromotive force, i. e., the 
size of grain, depth of paste, influence of diffusion and influence of 
impurities. A determination of the temperature coefficients will 
also be made. 

GENERAL CONCLUSIONS. 

The principal conclusions to be drawn are — 
I. That samples of mercurous sulphate of uniform electromotive 
properties can be prepared by a number of different methods. 



72 Bulletin of the Bureau of Standards, \voi.4,no.i. 

2. The remaining materials used in the construction of standard 
cells can easily be obtained in an exceedingly pure state, and, besides, 
the ordinary impurities even in relatively large quantity, exert prac- 
tically no influence on the electromotive force, so that Clark and 
Weston standard cells are reproducible to within 2 or 3 parts in 
100,000. 

3. When set up with proper materials the cells generally reach a 
practically constant value within a few days, and the electromotive 
force of both types can be depended on well within the above limits 
for at least one year. 

4. The close agreement of the numerous samples prepared by dif- 
ferent methods and under varying conditions shows that any effect 
due to size of grain may be disregarded. 

5. The results obtained with exchange cells and samples of mer- 
curous sulphate further establish the reproducibility of the cell. 

6. Our experience with exchange cells, sent to and received from 
other investigators, shows that with ordinarj'^ precautions cells may 
be transported considerable distances without influencing the elec- 
tromotive force. 

7. The labor of preparing suitable materials for use in standard 
cells is much greater than the work of setting up the cells when all 
materials are ready. If these materials were to be furnished by the 
various national physical laboratories, standard cells could be set up 
by any investigator in a very short time, and the standard cell could 
well serve as one of the two fundamental electrical standards. 

If the ampere as defined by the quantity of silver deposited per 
second were to be chosen as one of the two fundamental units (the 
ohm being the other), the standard cell would have to be depended 
upon between coulometer measurements to maintain the standard. 
Inasmuch as these measurements are somewhat laborious it is prob- 
able that they would be made quite infrequently. The standard cell 
has, however, shown itself to be sufficiently constant to justify trust- 
ing it for considerable periods, and if new cells set up occasionally 
agree with the old it would be necessary to resort to silver coulo- 
meter measurements only at considerable periods of time. This 
suggests, indeed, that the use of the silver coulometer as one of the 
two fundamental standards is of doubtful utility, as it seems improb- 
able that it has sufficient advantage from the point of view of repro- 



^^£rs] Clark and Weston Standard Cells, 73 

ducibility (if, indeed, it is as reproducible as the standard cell) to 
compensate for its greater inconvenience. 

In the opinion of the authors the standard cell is to be preferred 
to the silver coulometer for another reason, namely, that practically 
all voltage and current measurements of precision are made by the 
potentiometer method, and thus directly in terms of the standard cell 
or a combination of a standard cell and a standard resistance. 

The authors wish to acknowledge the valuable assistance rendered 
by Mr. M. P. Shoemaker, both in the preparation of the cells and in 
the electrical measurements. 



APPENDIX. 



Report on Standard Celi^ Exchanged with Foreign Labo- 
ratories. 

On May 9, 1907, twelve Clark and twelve Weston cells, which 
had been set up at the Bureau of Standards and kept under observa- 
tion for some time, were taken abroad by Dr. G. K. Burgess of this 
Bureau. They were carefully packed in tin cases after being sepa- 
rately wrapped in cotton and paraffined paper. The cans were car- 
ried by hand in a traveling bag, and kept in an upright position 
during transit. Rough weather was encountered for about three 
days, both on the outgoing and the return ocean passages. Six of 
the cells, three Clark and three Weston, were constructed with the 
aim of securing portability by the aid of an asbestos plug in each 
limb, held in place by a perforated glass tube fused to the cell walls. 

Comparisons of all the cells were/ first made at the English 
National Physical Laboratory between May 25 and May 31, the 
Weston cells being compared with an equal number of cells of the 
same type, set up by Mr. F. E. Smith, four of which were kindly 
given the Bureau of Standards and four each to the Reichsanstalt 
and to Professor Mascart. The results show that the mean value 
of the Bureau Weston cells is less by three microvolts than the mean 
of the National Physical Laboratory cells with which they were 
compared. The results given in the tables were reduced to the 
Bureau basis of comparison by the aid of the measurements made 



74 Bulletin of the Bureau of Standards, [Voi. 4.^0.1. 

May 9 and August 22 on six of the Weston cells which were brought 
back to Washington. 

According to a letter from Mr. Smith, the mean of all the Weston 
cells (more than icx)) of the National Physical Laboratory' is about 
20 microvolts greater than the mean of the Bureau cells compared, 
so that the mean of all would be about 10 microvolts greater than 
the Bureau basis of reference, which, as stated above, is the mean 
of twelve Weston cells set up in May, 1906. 

Eight of the Bureau Weston cells were next measured at the 
Laboratoire Central d']felectricit6 " under conditions which allowed 
an approximation to i part in ico,oco." The maximum deviation 
of these cells from their mean was found to be 0.00002 volt, and the 
difference between this mean and the mean of the Weston standard 
cells of the Laboratoire Central was found to be of the order of 
o.ooooi volt. Eight of the English Weston cells compared under 
the same conditions showed a maximum deviation from their mean 
of about 0.00003 volt, and their mean differed from the mean of the 
Weston cells of the Laboratoire Central by about 0.00001 volt. A 
second set of comparisons, made at Paris in August and for which 
a formal report has not yet been received, confirms the first meas- 
urements on the Bureau cells, while four Weston cells constructed 
at the National Physical Laboratory had a mean electromotive force 
about 0.00003 volt greater than the mean of those of the Laboratoire 
Central d'Electricit^. The above comparisons were made in kero- 
sene baths which were stirred during the measurements. No tem- 
perature control was provided, so that the differences found may be 
partly accounted for by a slight hysteresis. Eight of the Weston 
cells of the Bureau and eight of the English cells were compared at 
Berlin, June 20 and 21, between the two comparisons at Paris. A 
preliminary report of the measurements made at Berlin has been 
received with the request to withhold publication for the present, so 
that the results of comparisons with the Reichsanstalt cells are 
omitted. We have, however, taken the liberty of calculating the 
relative values of the Bureau and the National Physical Laboratory 
cells to our basis of reference by the aid of measurements made May 
9 and August 22 on Weston cells 105, P8, P9, Pio, and 187, assum- 
ing the small rate of change in their mean to have been unifonn in 
the interval. The comparisons at the National Physical Laboratory'' 



{J^j'^j] Clark and Weston Standard Cells, 75 

were reduced in the same manner. Two Weston cells were kindly 
placed at the disposal of the Bureau by the Laboratoire Central 
d'6lectricit6 and two by the Reichsanstalt. 

Clark cells, — No measurements on the Clark cells were made at 
the Laboratoire Central d'Electricit^. Those at the National Phys- 
ical Laboratory showed a discrepancy in cells 35 and 28a, set up 
April 12, 1906, and November 23, 1906, respectively. As these 
measurements were not made in a thermostatically controlled bath, 
and as, in addition, the first measurements made on their return to 
Washington show similar differences, it is highly probable that the 
discrepancy of May 25-31 is due to hysteresis, which would be 
greater in the older cells, the others having been set up April 30, 
1907. The comparisons made in Washington on May 9 on cells 
35, 28a, 97, 98, 99, and 109, before their departure, and on August 
22 on their return, show that the average change of the Clark cells 
has been even less than that of the Weston cells. The measure- 
ments made at London and Berlin were reduced to the Bureau basis 
in the same manner as described above for the Weston cells. 

In the accompanying Tables XIX and XX, column i gives the 
numbers of the cells, column 2 the dates on which they were set 
up, columns 3, 4, 5, and 6 data in reference to the materials employed, 
and the remaining columns the differences in microvolts from the 
mean of twelve Weston cells and five Clark cells taken respect- 
ively as the basis of reference. The comparisons on May 9 and 
August 22 of the six Weston cells which had been measured at the 
three foreign laboratories show a mean decrease of six microvolts on 
their return to Washington, the change in only one cell exceeding 
ten microvolts. Practically all of the change of the cells set up 
April, 1907, is to be attributed to a small decrease frequently 
observed in cells newly set up, as is shown by check cells set up at 
the same time which remained in Washington. The Weston table 
includes the measurements on the exchange cells made immediately 
after their receipt at the Bureau. It will be noted that one of the 
cells of the National Physical Laboratory had a somewhat high 
initial value, but is rapidly approaching the mean of its companion 
cells. 

The measurements on the two cells received from the Reichsan- 
stalt are also given for the sake of completeness, although, on account 



Bulletin of the Bureau of Standards, 
TABLE XIX. 



lVoL4,No.t. 



Tabulation of Results. 
Wesion Cells — Differences in microvolts from mean of reference cells. 



Cell 


Date 




Hb,S04 


CdSOf 


Cd-Amalg. 


1 

.A 
>. 

9 


J? 

i 


« 
% 

2 


1 
s 

i 


M 


s 


19 


June 22, 


»06 


D-9.25V=.5 


Ka]il.2Clondy 


12i4Kahl.El. 


- 9 


- 7 - 7 - 4 


-8-7 


105 


June 27, 


>06 


Longe IV 


i< 1 II 


-11 


-161-17 -15 
% ^ ^ 


-19 -18 

w 1 oo 














% 


lit 


II 


P8 


April 13, 


'07 


^1 Dec. 21, '06 Katal.3C]oudy 


l2i<Kahl.Bl. 


- 8 




- 7 -10 


- 8 - 3 


P9 


<< 




l:6HtS04 








13 




-12 -13 


-11 - 7 


PIQ 


** 




. D=5.25 




' 




-13 





-12 1 -12 


-11-7 


»P11 


II 




II 








- 9 




-8-9 


-7|-4 


»P12 


9 

II 




It 








-13 




-12 1 -13 


-11 - 6 


1P13 


II 




it 








-10 




-11 -11 


-9-6 


181 


April 30, 


'07 


r#2Dec.2i,'06 










+12 


+ 8,+ 3 


+ 4;+! 


182 


II 




l:6HsS04 










+ 6 


+ 3' 


+ 2!-3 


183 


«< 




I D-5.25 










+ 5 


+ 4-2 


01+4 


184 


II 




II 










+ 8 -1- 7' t 1 


+ 3,+ 4 


185 


II 




II 










+ 6+10+5 


+ 6+5 


186 


<i 




'* 










-1 -2'-8 


-5-2 


^87 


«« 




11 






.*' . 




+ 5+4 +1 


+ 3i+5 


M88 


II 




11 






II 




+ 4 +3-2 


- 1 


H26 


Feb., 


'07 
















C19 


June, 


>06 


« 














P53 


H07., 


'06 


1 
















P54 


Hov^., 


'06 














1 


P55 


Hov^., 


'06 














1 


C12 


June, 


'06 


% 


,8et up at the National Phys- 










1 


C117 


June, 


'06 


t 


ical Labozatoiy 












H29 


Feb., 


'07 
















P210 


Mar., 


'07 


1 
















H28 


Feb., 


'07 


Q 
















C17 


June, 


'06 


- 














1 


P52 


H07., 


'06 
















i 


1 
02 


Pasted 


iatni 


bed in tnnBit 


rset up at Physikalisch-Tedi- 

1 niscfae Reichsanstalt 

1 














P.C.N.4 








Set up at Laboiatoire Gential 
d'filActricitA 














P.C.N.6 




































* Cells which remained at the Bureau of Standards. 



fVoiff. 1 
Waters.} 



IVoi 



Clark and Weston Standard Cells. 

TABLE XIX. 

Tabulation of Results. 

Weston Cells — Differences in microvolts from mean of reference cells. 



n 




PS 

P9 

PIO 
IPU 
1P12 
1P13 

181 

182 

183 

184 

185 

186 

187 
1188 

H26 

Cl9 

P53 

P54 

PS5 

C12 

C117 

H29 

P210 

H28 

C17 

PS2 

01 
02 

P.aH.4 
P.CJf.6 



- 8 
-10 
-10 



2-^ 






- 5 



- 7 

+ 6 







+ 1 

+ 6 
9 




< 



(-17) 
(-17) 



(- 7) 
(-10) 
(-12) 



s 


5? 


« 


^ 


< 


< 


1 


< 


-22 


-23 


-25 


-30 


-22 


-23 


-25 


-23 


-13 


-12 


-13 


-15 


-16 


-16 


-16 


-17 


-16 


-16 


-16 


-17 


-15 


-15 


-15 


-16 


-15 


-13 


-14 


-16 


-16 


-14 


-16 


-17 



-26 
-17 



- 7 
-15 
-15 
-13 
-12 
-15 



Left at National Physical Laboiatoiy 

JLeft at Physikaliadi-TeOluiiBCtae Reiclis- 
J anstalt 

iLeft at the Laboratoiie Centxal d'filectricitd 



(-5) 


- 6 


- 6 


- 7 


- 7 


- 4 




-10 


-9 


-10 


-10 


- 7 


(+5) 


- 4 


-11 


-16 


-17 


-15 


(+78) 


+36 


+15 


- 6 


-12 


-15 


(+3) 


- 4 


- 5 


- 8 


- 7 


- 5 


(+2) 


- 3 


- 3 


- 6 


- 7 


- 4 



Left at Physlkallsch-Techiiische RAlchaaiistalt 



Left at Lahoiatoiie Central d'6leetrlcit6 



I 



(+338) 
(+93) 
(+ 8) 
(- 9) 



+246 
+ 86 

+ 5 

- 25 



+169 
+ 86 

+ 2 
- 28 



+90 
+78 

+ 4 
-28 



+70 +47 

+71 +63 



+ 4 
-30 



-10 
-25 



' Observations made ten minutes after cells had been put in bath. The values 
given represent the differences, in microvolts, between the individual cells and the 
mean of twelve cells of the same type taken as the basis of reference. 
8919 — 07— -6 



78 Bulletin of the Bureau of Standards. \voi, 4. No. t. 

TABLE XX. 
Tabulation of Results. 
Clark Cells. — Deferences in microvolts from mean of reference cells. 













1 






1 






Cell 


Dftte 


Hb804 


Zn804 


Zn Amulg. 


8 


< 


•1 

1 




M 

1 


8 


35 


April 12, *06 


D- 1 ▼-.75 


^TrnMhrnmn 


lOjCKaU.^l 


+ 4 


+ 5 


+ 5 


+ 7 


+ 8 


+11 


28a 


irov. 23, '06 


D-.2 ▼-.5 


It 


II 








+ 2 


+ 3 


+ 3 












? 


1 


1 


1 


m 

1 


Ok 


97 


April 30, '07 


f<pDec.21,'06 


Baker ciyt- 






+ 7 


+ 5 


+ 4 


+ 2 


+ 3 


+ 2 


96 




l:6H«804 


tala audio- 






+ 5 


+ 3 


+ 4 


+ 2 


+ 2 


+ 1 


99 




I D-5.25 


1 tatton 






+ 9 


+ 9 


+10 


+ 7 


+ 7 


+ 7 


noo 




<f 










+ 9 


+ 8 


+ • 


+ 7 


+ 5 


MOl 




" 










+ 4 


+14 


+12 


+ 8 


+ 9 


+ 9 


103 




it 










+15 


+15 


+14 


+16 


+16 


+11 


104 




It 










+ 8'+10 


+ 9 


+10 


+11 


+ 9 


105 




n 










+ 8|+ 8 


+ 5 


+ 5 


+ 5 


+ 2 


106 




f f 










+10 


+10 


+ 9 


+11 


+11 


+ 9 


107 




<f 










+14 


+14 


+10 


+10 


+13 


+10 


106 




<< 










+ 3 


+ 3 


+ 1 


+ 2 


+ 4 


+ 2 


109 




II 










+ 6 


+ 9 


+ 7 


+ 7 


+ 7 


+ 8 


MIO 




II 


II 1 

1 




+13 


+14 


+12 


+10 


+11 


+11 



^ Cells which remained at the Bureau of Standards. 



Wolff. 1 
Waters.} 



Clark and Weston Standard Cells. 
TABLE XX. 
Tabulation of Results. 
Ocark Cells, — Differences in microvolts from mean of reference cells. 



79 



c^ 


1 


1* 




M 


s 
8 

9 


•-» 


Q 


1 


•• 
8 

1 


s? 

9 
< 


It 

i 


t 


M 

1 


35 

97 

98 

99 

1100 

um 

109 
104 

106 
107 
108 
109 

UIO 


+1 

+3 
+6 


(-53) 
(-56) 

+ 1 
+ 4 
+ 7 








+9 






(-15) 
(-45) 

(+4) 

(+1) 

(+ 1) 

+ 1 

+ 9 


+3 
-3 

+5 
+3 
-2 

+1 

+9 


+2 
-3 

+8 
+6 
+1 
+1 
+9 



-4 

+6 
+5 

+1 



+9 


—1 








-2 

+9 

+2 


1 


_5 








J 
1 


+6 








1 


+5 

+2 


1 












+1 
+7 






+8 


-1 

+7 
1 





+ 3 
+ 3 
+ 6 
+ 7 
+ 5 
+ 2 
+ 6 


+6 




+8 








1 


Left at Natfonal Physical Laboiatmy 

1 








—8 ' 


















Left at Laboiatoiie Centxal d']ftlectricit6 








1 








+2 






(-9) 
+ 9 


+4 
+9 


+7 
+9 


+7 * 
+8 


+6 


+8 




+7 


+8 +7 


+8 



' Measurements made within two hours after placing cells in bath. The values 
given represent the differences, in iHicrovolts, between the individual cells and the 
mean of five cells of the same type taken as the basis of reference. 



8o Bulletin of the Bureau of Standards. \yoi. 4. no. i. 

of the fact that the paste in both had evidently been disturbed in 
transit, they should not be considered as throwing any light on the 
question of reproducibility. The cells received from the Laboratoire 
Central d'^lectricit6 show a most satisfactory agreement with the 
Bureau cells and with those received from the National Physical 
Ivaborator>% 

The conclusions to be drawn are: 

(i) That standard cells can be set up by different investigators 
with different materials which agree to within a few parts in 100,000. 

(2) That standard cells can be constructed which show no appre- 
ciable change when carried considerable distances, even on ship- 
board, provided ordinary precautions are observed. 

Washington, September 17, 1907. 



THE ELECTRODE EQUILIBRIUM OF THE STANDARD CELL 



F. A. Wolff and C. E. Waters.* 



Some experiments described by Hulett " indicating the existence 
of a state of unstable equilibrium in the Weston cell have, on 
account of the importance of the subject, led to a further study of 
the question at the Bureau of Standards. 

The equilibrium between cadmium amalgam and cadmium sul- 
phate was first studied. Saturated solutions of the latter were shaken 
up in air, nitrogen, hydrogen, and in vacuo with cadmium amalgam, 
but in no case did the electromotive force of cells set up with the 
treated and untreated solutions differ more than lo microvolts, even 
though the samples shaken in the presence of air had become cloudy 
from the formation of an excess of basic cadmium sulphate. 

The equilibrium of the system mercury, mercurous sulphate, cad- 
mium sulphate, and of the corresponding system of the Clark cell 
was then studied in special cells, so constructed that the above 
materials could be rotated and the effect determined without open- 
ing the cell. 

This consisted of a tube about 2 cm in diameter and 12 cm long, 
provided at the lower end with a small bulb into which a platinum 
wire was sealed. The bulb was connected to the main tube by a 
narrow neck, so that, with sufficient mercury in the cell, the plati- 
num terminal was not in contact with the solution, even during 
rotation. 



* An abstract of this paper was read at the New York meeting of the American 
Physical Society, December, 1906, Phys. Rev., 24, 251; 1907. 
•Phys. Rev., 28, 166; 1906. 

81 



82 Bulletin of the Bureau of Standards, ivoi.4.No.t. 

A shorter internal tube about i cm in diameter with several 
lateral openings, sealed in at the other end of the main tube, was 
charged with amalgam and crystals of cadmium or zinc sulphate, 
which were held in place by a plug of asbestos. Contact with the 
amalgam was made by means of a platinum wire, protected from the 
solution by sealing it into a glass tube, which extended through the 
upper seal made after the introduction of the above materials. 

The mercurous sulphate and cadmium sulphate or zinc sulphate 
crj'stals were introduced over the mercury through a side tube by 
which the cell was exhausted and through which a saturated solu- 
tion of cadmium or zinc sulphate was subsequently introduced. 
After filling, the side tube was sealed off, leaving only a small air 
bubble in the cell, thus practically eliminating any possible influ- 
ence of air. 

The cells were then placed in holders so arranged that one dozen 
could be simultaneously rotated at any desired speed, with their axes 
parallel to the axis of rotation and inclined at a small angle to the 
horizontal, thus insuring a thorough stirring of the paste and mer- 
cury with the electrolyte, even at five or six revolutions per minute. 
The measurements were made in an automatically controlled oil 
bath at 25°, immediately after stopping the rotation and raising the 
holder to a vertical position under the oil. Altogether 12 Weston 
and 5 Clark cells of this type were set up with samples of mercurous 
sulphate, made not only by the electrolytic method but also by sev- 
eral chemical methods. The mercurous sulphate was washed in a 
Gooch crucible three times with i : 6 sulphuric acid, six times with 
absolute alcohol, and three times with saturated zinc or cadmium 
sulphate solution. The data and results are given in the following 
tables: 



WaUn^ 



Electrode Equilibrium of Standard Cell, 
TABLE I. 
Weston Rotating Cells. 



83 









1 






Hg^04 




Date 

1900 


Cd804 


Cd 
Amalff. I Mercury 








c^ 


Sample 


Method of Preparation 


K 1 


Oct.l3 


Puilfledby 
Racrys- 
tallisa- 
tion. 


121 f(Kaia.l Distilled 

Bl.DiBt. atreduoed 

piMsure. 


b,8 


gray 


EtoctnOytic (D-5; V-.5) 


«&11 


Oct.30 


(1 


*' 


" 


bi. 


gray 


meetitflytic (D-5; ¥-.5) 


tai2 


Oct.30 


<( 


1 1 


II 


b„ 


pay 


Blectrolytlc (D-5; V^.S) 


K 3 


Oet.l3 


II 


i< 


II 


e. 


gray 


By action of HN A and H^4<m Hg 


K 5 


Oct.l6 


II 


" 


it 


d. 


gray 


ProinHgffOsajidSi804 


K 6 


Oet.l6 


*' 


** 


II 


c 


gray 


By action of fuming Hf804 on Hg 


K 2 


Oct.l3 


II 


.. 


«« 


a It 


white 




t»8 
R 4 


Oet.30 
Oet.16 




:: 


II 


*1S 

a» 


white 
white 


Blectnflytic (D-.25 1:16 H^SOf) 


}R10 


Oct.30 


II 


11 11 


a» 


white 




R 7 
XR9 


Oet.16 
Oct.30 


II 
II 


II i( 

II 1 II 

1 


it 
it 


white 
white 


By d^Mtionof Ooml. Sample with 



* Platinum terminal exposed to paste, 
t Basic cadmium sulphate added to paste. 

I Iffercuroua sulphate rotated with saturated CdS04 solution 2I days before its introduction into 
theceUa. 









TABI.K II. 












Clark Rotating Cells. 




Cell 


Date 
xgo6 


Zn804 


Zn 
Amalg. 


Mercury 






Hg^04 


Sample 


Method of Preparation 


R2 


Ner.5 


Pnrifled by 
Beetmlysis 


Kahl.I 


IMatiUed 
atnduoed 
pieeeoie 


b,. 


gray 


Blectrtlytic (D=9.25: V=.75) 


«R3 


«dT.5 


II 


II 


I* 


wb 


gray 


BiBCtndytIc (D-9.2S; T-.TS) 


R5 
•R4 




i< 


II 
<i 


II 


ais 
ati 


white 
white 


Blectndytic (D-.25; 1:6 B. 
8O4) 


Rl 


IIOW.5 


it 


II 


II 


a* 


white 



* Zinc oxide added to paste. 



84 



Bulletin of the Bureau of Standards, 

TABLE in. 

Weston Rotation Cells. 

[Differences in microvolts from mean of reference cells.] 



{Vol. 4^^0.1. 



Date 


Rl 


Rll 


R12 


R3 


R5 


R6 
































Diff. 


Time 


Dlff. 


Time 


Diff. 


Time 


Diff. 


Time 


Diff. 


Time 


Diff. 


Time 






D. 






D. 


H. 




D. H. 




D. H. 




D. H. 




D. H. 


Oct. 18/06 


+72 

+43 
+11 
















+89 
+59 






+ 83 
+ 59 






+92 
+67 






<i 19 










** 20 














+24 





+ 34 





+39 





<« 22 ■ 


+29 
+44 














+39 





+ 54 





+55 





*' 23 














+53 


15 


+ 57 


15 


+66 


15 


ff 24 


+42 
+45 
+63 
+88 
+61 














+57 


18 


+ 88 


18 


+43 


18 


«* 25 


1 












+41 


1 9 


4103 


1 9 


+41 


1 9 


** 27 


3 












+64 


3 1 


+142 


3 1 


+58 


3 1 


** 29 


5 












+88 


5 1 


+149 


5 1 


+83 

+56 


5 1 


<« 31 


6 




- 4 







-11 





+69 


6 21 


+ 93 


6 21 


6 21 


Nov. 5 


+73 


10 




+ 55 


3 


7 


+37 


3 7 


+83 


10 14 


+ 90 


10 14 


+65 


10 14 


«« 8 


+66 


12 




+ 79 


5 


11 


-17 


5 11 


+67 


12 17 


+^04 


12 17 


+46 


12 17 


" 12 


+72 


16 




+ 69 


9 





-31 


9 6 


+69 


16 12 


+ 71 


16 12 


+52 


16 12 


«* 16 


+64 


20 




+ 116 


12 


20 


-54 


13 2 


+70 


20 8 


+ 50 


20 8 


+55 


20 8 


'« 19 


+59 


23 




+ 139 


15 


17 


-36 


15 23 


+69 


23 5 


+ 47 


23 5 


+54 


23 5 


<< 24 


+50 


28 




+ 204 


20 


16 


-26 


20 22 


+71 


28 4 


+ 41 


28 4 


+54 


28 4 


«' 30 


+35 


28 




+ 117 


20 


20 


-37 


21 2 


+35 


28 8 


+ 29 


28 8 


+32 


28 8 


Dee. 5 


+31 


28 




+ 93 


20 


20 


-39 


21 2 


+33 


28 8 


+ 26 


28 8 


+30 


28 8 


«« 10 


+46 


32 




+ 240 


24 


13 


- 8 


24 19 


+74 


32 1 


+ 40 


32 1 


+54 


32 1 


«* 14 


+50 


35 




+ 271 


28 


4 


-25 


28 10 


+74 


35 16 


+ 45 


35 16 


+53 


35 16 


«i 21 








+ 348 


33 


21 


-17 


34 12 


+92 


41 18 


+ 41 


41 18 


+38 


41 18 


Jan. 5,»07 






+ 520 


46 


12 


-32 


47 3 


+67 


54 7 


+ 41 


54 7 


+19 


54 7 


'* 10 






+ 567 


50 


6 


-27 


51 20 


+66 


59 4 


+ 47 


59 4 


+28 


59 4 


«* 14 






+ 427 
+ 749 


52 
61 


18 
1? 


-34 
-26 


54 8 
62 16 


+51 

+66 


61 16 
70 


+ 40 
+ 46 


61 16 
70 


+13 
+33 
+24 
+32 
+28 


61 16 
70 


i« 24 






i< 30 






+ 926 


67 


7, 


-36 


68 6 


+50 


75 22 


+ 42 


75 22 


75 22 


Feb. 5 






+1030 


71 


10 


-36 


73 6 


+49 


80 21 


+ 37 


80 21 


80 21 


** 8 






+1073 


7? 


71 


-35 


74 18 


+46 


82 9 


+ 38 


82 9 


82 9 


Kar. 1 












-43 


93 14 


-38 


101 5 


+ 38 


101 5 


+35 
+40 


101 5 


i« 12 










-42 


102 14 


-29 


110 5 


+ 32 


110 5 


110 5 


Apr. 5 
*« 10 










—41 


121 4 




128 19 


+ 90 


128 19 


+51 


128 19 










-34 


124 10 


—10 


132 1 


+ 94 


132 1 


+76 
+84 
+95 
+94 

+99 


132 1 


May 25 
June 4 










—38 


135 4 




142 19 


+127 


142 19 


142 19 
152 11 




1 




-34 


144 20 




152 11 


+135 


152 11 




1 




-37 


147 18 


+ 2 


155 9 


+142 


155 9 


155 9 
162 21 


*« 15 










—37 


155 6 




162 21 


+169 
+ 44 


162 21 


Aiig.15 








+ 494 


72 


21 


-40 


155 6 


— 5 


162 21 


162 21 


+43 


162 21 


Sept.27 








+ 571 


72 


21 


-41 


155 6 


— 6 


162 21 


+ 38 


162 21 


+23 


162 21 







Waters.} 



Electrode Equilibrium of Standard Cell. 
TABLE III. 
Weston Rotation Cells. 

[Differences in mlcroTolts from mean of reference cells.] 



85 



R2 


R8 


R4 




RIO 




R7 


R9 


Dlff. 


Time 


Dlff. 


Time 


Diif. 


Time 


DifT. 


Time 


DifT. 


Time 


DifT. 


Time 




D. 


H. 




D. 


H. 




D. 






D. 


H. 




D. 


H. 




D. H. 


+M8 
+115 
+ 59 
+ 98 
+103 
+220 
+275 
+245 
+313 














+ 137 
+ 100 
+ 69 
+ 94 
+ 95 
+ 252 
+ 354 
+ 316 
+ 363 
+ 441 












+ 93 
+ 49 









































+ 10 









































\^ 














+ 46 




\S 








18 














+115 




18 






1 


q 






1 








+173 


1 


19 






3 


1 






3 








+168 


3 


Q 






5 


1 






5 








+178 


•» 


9 






+321 


6 


21 


- 9 







6 




+216 







+111 


7 


5 


+ 76 





+340 


10 


14 


+515 


3 


7 


+ 440 


10 




+590 


3 


7 


+187 


10 


22 


+295 


3 7 


+329 


12 


17 


+474 


5 


11 


+ 572 


12 




+556 


5 


11 


+141 


13 


2 


+249 


5 11 


+292 


16 


12 


+389 


9 





+ 429 


16 




+501 


9 





+ 97 


16 





+186 


9 


+279 


20 


8 


+380 


12 


20 


+ 810 


20 




+440 


12 


20 


+ 90 


19 


20 


+187 


12 20 


+259 


23 


5 


+414 


15 


17 


+ 754 


23 




+479 


15 


17 


+ 81 


22 


16 


+159 


15 17 


+237 


28 


4 


+364 


20 


16 


+ 754 


28 




+389 


20 


16 


+ 61 


27 


16 


+104 


20 16 


+152 


28 


8 


+272 


20 


20 


+ 655 


28 




+265 


20 


20 


+ 57 


27 


19 


+ 93 


20 20 


+136 


28 


8 


+228 


20 


20 


+ 613 


28 




+234 


20 


20 


+ 52 


27 


19 


+ 85 


20 20 


+204 


32 


1 


+337 


24 


13 


+ 931 


32 




+336 


24 


13 


+ 69 


31 


12 


+107 


24 13 


+194 


35 


16 


+336 


28 


4 


+1092 


35 


16 


+314 


28 


4 


+ 68 


35 


3 


+106 


28 4 


+191 
+150 
+147 


41 
54 

59 


18 
7 

4 














+248 
+207 
+207 


33 
46 
50 


21 
12 
6 


+ 74 
+ 63 
+ 58 


40 
53 
57 


20 
12 

6 


+ 95 
+ 63 
+ 72 


33 21 










46 12 











50 6 


+126 
+ 56 

+110 


61 
W 
75 


16 
22 










+195 
+196 
+146 


52 
61 
67 


18 
12 
2 


+ 70 
+ 73 
+ 50 


59 
68 
74 


17 
12 
2 


+ 53 
+ 72 
+ 36 


52 18 










61 12 










67 2 


+115 


80 


21 










+135 


71 


10 


+ 44 


78 


10 


+ 38 


71 10 


+113 
+118 


82 
101 












+139 


72 


21 


+ 45 


79 


21 


+ 33 


72 21 












+ 60 
+115 


110 
























128 


19 
















1 






+114 


132 
















1 






+113 
+115 
+111 
+135 


142 


19 


1 












1 1 




152 


11 
















1 1 




155 


















i;:::;':. 1 




162 


21 
















1 






+ 15 
+ 7 


162 
162 


21 
21 










+ 55 
+ 55 


72 
72 


21 
21 


+ 36 
+ 28 


79 
79 


21 
21 


+ 12 

+ 13 


72 21 










72 21 













86 



Bulletin of the Bureau of Standards. 

TABLE IV. 

Clark Rotation Cells. 

[Differencea in microTolU from mean of reference cells.] 



\yol,4.No,i, 







R2 






R3 






R5 




R4 




Rl 


Date 






















. — 


- 
































Dlff. 


Time 


Diff. 


Time 


Diff. 


Time 


Diff. 


Time 


Diff. 


Time 






D. 


H. 




D. 


H. 




D. 


H. 




D. 


H. 




D. H. 


Hov. 6,*06 


-25 







-120 















-140 







+ 13 





Hov. 7 


-13 




22 


-130 




22 


+ 30 




22 


- 50 




22 


+ 27 


22 


Hov. 8 


+16 


1 


22 


- 54 


1 


22 


+ 59 


1 


22 


- 26 


1 


22 


+ 49 


1 22 


Nov. 12 


+16 


4 


16 


+ 45 


4 


16 


+100 


4 


16 


+ 25 


4 


16 


+ 90 


4 16 


Nov. 16 


+17 


8 


13 


+ 2 


8 


13 


+ 89 


8 


13 


+ 2 


8 


13 


+ 72 


8 13 


Nov. 24 


+21 


16 


9 


+ 4 


16 


9 


+ 89 


16 


9 


± 


16 


9 


+ 81 


16 9 


irov.30 


+36 


16 


12 


+ 18 


16 


12 


+ 61 


16 


12 


- 5 


16 


« 


+ 46 


16 12 


Dec. 5 


+22 


16 


12 


- 20 


16 


12 


+ 45 


16 


12 


- 43 


16 


12 


+ 22 


16 12 


Dec. 10 


+22 


20 


6 


+202 


20 


6 


+ 72 


20 


6 


- 34 


20 


6 


+ 22 


20 6 


Dec. 14 


+21 


23 


20 


+273 


23 


20 


+113 


23 


20 


+ 98 


23 


20 


+ 8 


23 20 


Dee. 21 


+26 


29 


22 


+ 22 


29 


22 


+ 34 


29 


22 


+ 20 


29 


22 


- 36 


29 22 


Jan. 5, '07 
Jan. 10 








-217 
-243 


42 

47 


14 
10 


-136 
-141 


42 

47 


14 
10 


- 17 

- 3 


42 

47 


14 
10 


+ 12 
+ 7 


42 14 






47 10 


Jan. 14 






-160 


49 


22 


-199 


49 


22 


- 50 


49 


22 


- 99 


49 22 


Jan. 24 






+ 5 


58 


7 


- 5 


58 


7 


- 47 


58 


7 


+157 


58 7 


Jan. 30 






+ 20 


64 


4 


-159 


64 


4 


- 35 


64 


4 


- 33 


64 4 


Feb. 5 






+ 16 


69 


4 


-155 


69 


4 


- 26 


69 


4 


- 48 


69 4 


Feb. 8 






+ 17 
- 17 


70 
89 


16 
12 


-145 
-143 


70 
89 


16 
12 


- 23 

- 37 


70 
89 


16 
12 


- 4 

- 97 


70 16 


Kar. 1 


■( " 


89 12 


Mar. 12 


1 


- 20 


98 


12 


-182 


98 


12 


- 60 


98 


12 


-227 


98 12 


Apr. 5 


1 


- 88 


117 


2 


- 68 


117 


2 


- 28 


117 


2 


-108 


117 2 


Apr. 10 


1 


- 91 


120 


8 


- 59 


120 


8 


- 43 


120 


8 


-145 


120 8 


May 25 
June 4 


I 








- 76 


131 


? 


- 79 


131 


I 


+174 
—216 


131 2 


1 '" 


1 


- 91 


140 


18 


- 84 


140 


18 


140 18 


June 7 
June IS 


; 


- 47 


143 


16 


- 79 

- 86 


143 
151 


16 

4 


- 62 

- 76 


143 
151 


16 

4 






1 


+ 3 


151 4 


i 






m!urs^ Electrode Equilibrium of Standard Cell. 87 

It will be seen that no initial low values, as observed by Hulett, 
were obtained. The Weston cells with gray samples of mercurous 
sulphate show changes which do not exceed o.oi per cent even after 
continuing the rotation four months, except in one case in which 
the platinum terminal was purposely exposed. In this cell the 
terminal was inadvertently amalgamated, but was treated with aqua 
regia to remove the mercury before filling. The white samples 
generally showed considerably larger effects, but not as great as 
those observed by Hulett. There was also a tendency to reach a 
maximum value, and then, on further rotation, to approach the 
normal. 

Cell No. 1 2, in which basic cadmium sulphate* was added in excess 
to the cadmium sulphate solution, gave approximately normal results 
from the first, although the paste was quite yellow. 

Although the Clark cells showed smaller effects than the Weston 
cells, there seem to be slight differences produced by rotation. Cells 
3 and 4, in which an excess of zinc oxide was added to the zinc 
sulphate solution, showed only a slight difference ; but after an inter- 
ruption of the rotation for several days the paste caked and the 
results subsequently obtained were irregular. The irregularities of 
the remaining Clark cells subsequent to December 5 may possibly 
be due to the cracking of the protecting tube about the platinum 
wire imbedded in the amalgam. Owing to the construction em- 
ployed, this can not be determined without destroying the cell. 

On December 19, 1906, the Weston cells i, 4, and 8 were opened 
and the paste used in setting up cells of the ordinary form. The 
gray sample from cell No. i gave, after two days, practically the 
same value as in the rotating cell. It has slowly decreased and at 
present is within 25 microvolts of the normal. The two cells set 
up with the white samples showed abnormally high values, 600 and 
400 microvolts, respectively, both of which steadily decreased until 
March 25, 1907. On that date they were transferred from the bath 
in which they had been kept continuously at 25° to another at 20? 

'Made by adding sufficient ammonia to a solution of cadmium sulphate to dissolve 
the precipitate first formed, filtering into a large volume of water, collecting, wash- 
ing, and gently igniting the precipitate. 



88 Bulletin of the Bureau of Standards. \}'ol /, so. r. 

While only a very slight hysteresis was observed in the case of our 
Weston cells, particularly when finely crushed cadmium sulphate 
crystals were employed in the paste and over the amalgam, the two 
cells in question showed marked effects of this character. These 
persisted, with slight changes from day to day, for a long period, 
indicating either that a surface film was formed on the crystals 
during rotation or that a large excess of cadmium sulphate was 
employed in the paste, thus retarding the attainment of saturation 
equilibrium. A similar effect has been observed in a number of H 
cells in which the paste contained a large excess of cadmium sul- 
phate crystals. 

The results obtained show that not all samples of mercurous 
sulphate exhibit the behavior observed by Hulett, as gray samples, 
prepared by different methods, are changed by rotation for months 
by less than o.oi per cent.* This difference is. small enough to be 
possibly accounted for by attrition during rotation, thus introduc- 
ing the effect of size of grain, noticed by von Steinwehr. 

It does not appear to the authors that the high values shown by 
some of the rotation cells throw any light upon the decrease below 
the nonnal electromotive force observed by Hulett in some cells of 
the ordinary type. According to him the first reaction which takes 
place when the cell is set up is a hydrolysis by which the concen- 
tration of the mercury ions is increased. Opposing this is a reac- 
tion between the mercury and the products of hydrolysis in solu- 
tion, which reduces the concentration of the mercur>' ions. The 
secondary products formed in this reaction would, therefore, be 
responsible for the decrease observed by him in cells of the ordinary 
type. As it is evident that this effect can not be due directly to the 
formation of new mercury compounds in the presence of an excess 
of mercurous sulphate, since the concentration of the mercur>' ions 
would thereby be increased, it must, on this theory, be caused by 
other products of the reaction. 

In the rotation cells the amount of these secondary products would 
depend upon the duration of the rotation and on the area of the 
mercury surface exposed to the solution. According to Hulett's 

* While the samples of mercurous sulphate prepared by Hulett are in practical 
agreement with our own^ as shown by cells set up with exchange samples, his cells 
differ from those made at the Bureau by about one-third of the above amount. 



?f^£rs^ Electrode Equilibrium of Standard Cell. 89 

explanation, the slight effects observed by us with gray samples of 
mercurous sulphate, which owe their color to the presence of finely 
divided mercury, would be due, not to decreased hydrolysis, but to 
the acceleration of the secondary reaction. It would, therefore, 
follow that such samples should give abnormally low values after 
stopping the rotation. As in no case was this result obtained, the 
authors conclude that the effect must be due to some other cause. 

In view of the various questions which have arisen in connection 
with the results described in this paper, it is proposed to continue 
the investigation. 

Washington, October 4, 1907. 



A COMPARATIVE STUDY OF PLAIN AND FROSTED LAMPSJ 



Edward P. Hyde and F. E. Cady. 



Much attention has been given in recent years to the proper use 
of difiPusing globes around incandescent lamps. These globes have 
the twofold object of hiding from view the brilliant filament and of 
producing a more economical distribution of the light. It has 
usually been considered that the same general results could be 
obtained by frosting the bulb of the lamp, but this method has been 
called into question* principally on account of the relatively short 
useful life of frosted lamps. So far as the authors know, however, 
no systematic study of the effects of frosting incandescent lamps 
has ever been undertaken. Such an investigation was therefore 
outlined at the Bureau of Standards several years ago, and although 
many observations have been made the subject is by no means 
exhausted. 

These results of frosting may be classified under three general 
heads: (i) Change in Absorption; (2) Change in Distribution; (3) 
Change in Life. 

In conjunction with the study of the change in distribution many 
observations were made on the mean spherical reduction factors of a 
number of types of filaments. In fact, owing to the importance of 
this question in its bearing on the commercial rating of incandescent 
lamps on a basis of mean spherical candlepower, much attention was 
given to this part of the investigation. The results will, therefore, 
be discussed in a separate section of the paper. 

* Presented in abbreviated form under the title of "The Effect of Frosting Incan- 
descent Lamps*' before the National Electric Light Association, Washington, D. C, 
June 6, 1907. 

•Cravath and I^ansingh, Electrical World, March 17, 1906, p. 567. See also 
Electrical World, May 26, p. 1082, and June 23, p. 1304; 1906. 

91 



93 Bulletin of the Bureau of Standards. \voL4,no,2. 

1. APPABATUS AND METHODS. 

The principal apparatus employed in the investigation were a 
Reichsanstalt precision photometer bench on which the measure- 
ments of mean horizontal intensity and the determinations of dis- 
tribution curves were made, and a Matthews integrating photometer 
on which mean spherical candlepowers were obtained. The former 
instrument has been described fully in a previous paper.' The 
determination of mean horizontal candlepower was made in ever>' 
case by rotating the lamp about its axis at a speed of 200-250 r. p. m. 
In the case of lamps having a pronounced flicker at that speed a 
single auxiliary mirror, shown diagrammatically at M^ Fig. i, was 
used. As has already been pointed out by the writers in a paper* 
on the determination of the mean horizontal intensity of incandes- 
cent lamps by the rotating-lamp method, by combining on the 
photometer screen light emitted in two mutually perpendicular 
directions in the horizontal plane, the flicker due to the nonuniform- 

r . 

— © Fi^-- -e — 



Fig. 1. — Sketch Showing Stationary Auxiliary Mirror in Position, 

ity of the horizontal distribution curve of the lamp is greatly reduced, 
and accurate measurements can be made. Without some device of 
this kind it is impossible to obtain accurate results for certain types 
of lamps with the rotating-lamp method. In determining the mean 
vertical distribution curves of the lamps the speed of rotation was 
generally about 200-250 r. p. m. For lamps with pronounced 
flickers higher speeds were used, as it is impracticable to use the 
auxiliary mirror in these measurements. 

The universal rotator which was employed in determining the 
vertical distribution curves is shown in Fig. 2. This instrument 
has recently been designed and constructed in the instrument shop 
of the Bureau. The authors desire to acknowledge their indebted- 
ness to Mr. A. H. Schaaf and Mr. Oscar Lange for valuable aid in 
designing the instrument, and to Mr. R. Hellbach for painstaking 

•This BuHetin, 2, p. i; 1906. ♦This Bulletin, 2, p. 415; 1906. 



Bull. Bur. of Standards. 




Fig. 2. — Universal Rotator. 



Cad^'^ ^ Study of Plain and Frosted Lamps. 93 

care in constructing it. Inasmuch as there is not to be had, either 
in the United States or abroad, an entirely satisfactory universal 
rotator for laboratory purposes, it may not be amiss to describe here 
briefly the instrument made at the Bureau and used with entire 
satisfaction.* 

This instrument is so designed that it can be mounted directly on 
any standard photometer bench. As shown in Fig. 2, it is mounted 
on a standard carriage supplied with the Schmidt and Haensch pho- 
tometer. By the use of a counterpoise it is in equilibrium in all 
positions, and hence produces no strain on its support. The axis of 
rotation is horizontal at all times, permitting the use of mercury 
cups. If these are well made and well amalgamated the shaft can 
be driven at a speed of 500 or 600 revolutions per minute without 
throwing an appreciable quantity of mercury. Incandescent lamps 
of all sizes from 4 cp to 100 cp can be centered and measured, and 
even many of the ordinary shades and reflectors can be mounted 
with the lamps. 

Since there is no strain on any part of the instrument, a divided 
circle and index with clamp screw can be used instead of a notched 
wheel. This permits of angular settings with an accuracy of 10 or 
15 minutes for any desired angle, whether an even degree or a frac- 
tion of a degree. In most rotators on the market only angular 
settings at 5° intervals can be obtained, whereas it is frequently 
desirable to study distribution curves at much closer intervals in 
the neighborhood of rapidly changing curvatures. 

Finally, the instrument is provided with a second graduated circle 
at right angles to the other, so that the instrument can be used as a 
universal lamp support, as well as a universal rotator. Any angle of 
latitude or azimuth can be obtained, so that not only the vertical dis- 
tribution, but also the distribution in any latitude, can be determined. 

The Matthews integrating photometer which was used through- 
out the investigation is shown in Fig. 3. In general principle it is 
similar to that originally described by Professor Matthews,* but in 
detailed design it has been modified somewhat, both in theory and 

'The Bureau wiU be glad to furnish drawings of this instrument to anyone desir- 
ing them. 
•Proc. A. I. E. E., 20, p. 1465; 1902. 
8919-07 7 



94 Bulletin of the Bureau of Standards^ [voi, ^. Ai>. /. 

in mechanical construction. Instead of arranging the mirrors at 
equal angular intervals, beginning with one in the horizontal, use 
was made of the results of a previous theoretical investigation^ by 
one of the present authors. It was shown in that investigation by 
considering several simple cases of distribution curves, that the 
arrangement of mirrors completely satisfying Case III (/^ = cos d\ 
would best satisfy all practical cases. The mirrors were therefore 
placed at the respective angles deduced in the previous paper. 
According to this arrangement there is no mirror in the horizontal, 
but the mirrors are situated symmetrically in the two hemispheres, 
so that mean hemispherical as well as mean spherical intensities 
can be determined. 

The instrument shown in Fig. 3 was built in the instrument 
shop of the Bureau. It is loj^^ feet high and contains twenty 
pairs of mirrors. The lamp rotator, which is equipped with four 
mercury contacts, two for current, and two for potential leads, has 
two sockets, one upright and one inverted, so that lamps with soft 
filaments that will not support their own weight can be mounted, 
and even rotated at a low speed. The comparison lamp is mounted 
on a carriage which is moved back and forth by means of a pulley- 
wheel and steel tape. The latter, graduated in millimeters, passes 
under an index, from which the distance of the comparison lamp can 
be read. 

In using the instrument the substitution method is employed, 
i. e., a lamp, or number of standard lamps, whose mean spherical 
candlepowers are known, are first placed in the rotator and measured, 
and then the test lamps are substituted and measurements are made 
on them. A measurement consists in determining the distance at 
which a lamp known as the comparison lamp must be placed in order 
to secure a photometric balance. From the inverse ratios of the 
squares of the distances of the comparison lamp, corresponding to 
a photometric balance on the test and standard lamps, the mean 
spherical candlepower values of the test lamps in terms of the 
mean spherical candlepower values of the standard lamps can be 
computed. 

The adjustment of the mirrors is such that accurate ratios of 
mean spherical candlepower can be obtained even between lamps 

^This Bulletin, 1, p. 255; 1905. 




I 






/ 



A k. 



ff^ 



^^ 



A Study of Plain and Frosted Lamps. 



95 

with such widely different polar-distribution curves as the double 
filament lamp and the downward-light lamp. However, in order to 






TYPE A 



TYPE B 



TYPE C 





TYPE 



TYPE E 



TYPE F 



Fig. 4. — Types of Filaments Investigated, 

avoid any possible error that might result if the instrument were to 
get out of adjustment, the substitution method is carried further. 



96 Bulletin of the Bureau of Standards. \voi.4,No.r. 

In determining the mean spherical candlepower of lamps of any 
type of filament, lamps of a similar type of filament are used as 
standards. 

2. CHANGE m ABSORPTION. 

In studying the change in absorption due to frosting, six different 
types of lamps were used. These are shown in Fig. 4. The six 
types are as follows : Oval anchored (type A in the figure), double 
filament (type B), spiral filament (type C), double round coil (t>T)e D), 
double-flattened coil (type E), and downward-light filament (type F). 
Twenty-five i6-candlepower, iio-volt lamps of each type were 
obtained directly from the factories, and all were seasoned so that 
changes in candlepower would not occur during the investigation. 
Several lamps of each type were carefully calibrated for mean 
horizontal and mean spherical candlepower for use as standards for 
that type, and all subsequent measurements on lamps of any type 
were made in terms of the standards of the type. 

Each lot of lamps were measured for mean horizontal and meacn 
spherical intensity, and then sent to the factory to be frosted. After 
being returned from the factory the lamps were again measured 
for mean horizontal and mean spherical candlepower. The decrease 
in mean spherical intensity is taken as the change in absorption due 
to frosting. The decrease in intensity is spoken of as a change in 
absorption rather than as the absorption itself, because there is 
always some absorption in the glass even when there is no carbon 
deposit on the inside and no frosting on the outside of the bulb. 
The frosting can scarcely be said to absorb light by extinction, it 
merely diffuses it, and in this diffusion some luminous energy which 
otherwise would pass through the outer surface of the bulb is com- 
pelled to traverse the glass, and whatever deposit there may be on 
the inside of the glass, a third and fifth time, and thus suffer further 
absorption. It is probably not the frosted surface that absorbs the 
energy, however, but the glass, and the carbon deposit on the inside 
of the bulb. 



A Study of Plain and Frosted Lamps. 

TABLE I. 
Change in Absorption Due to Frosting. 



97 



Oval anchored 



Double 
filament 



Spiral 
filament 



Double 
round coil 



' Double flat- 
, ened coil 



Downvvard 
liiTht 



Lot I 


Lota 


Lota 


Lot 4 


Lots 


Lot 6 


Lot 7 


(add) 


(add) 


(add) 


(add) 


(add) 


(add) 


(add) 


3^ 


3!< 


5.5^ 


I'H 


yf> 


^ 


^ 


4 


3 


5.5 


2 


3.5 


4.5 




4 


3 


6 


3 


4 


4.5 




4.5 


3.5 


6 


3.5 


4.5 


5 




4.5 


3.5 


6.5 


4 


4.5 


5.5 




4.5 


4 


6.5 


4 


4.5 


5.5 




4.5 


4 


6.5 


4 


4.5 


5.5 




5 


4.5 


7.5 


4.5 


4.5 


5.5 




5 


4.5 


6.2)( 


4.5 


5 


5.5 




5 


5 




4.5 


5 


6 




5.5 







5 


5.5 


6 




5.5 


Z,Wi 




5 


5.5 


6 




6 


(■and) 


(■and) 


5.5 


6 


6.5 




6 


^ 


5.5^ 

6.5 


5.5 


6.5 


6.5 


8.5 


6 


5.5 


5.5 


7 


7 


8.5 


6.5 


5.5 


6.5 


6.5 




7.5 




6.5 


5.5 


6.5 


6.5 


4.95f 


8 





7 


5.5 


7 


6.5 




9 


7.5ji 


8 


5.5 


7.5 


7 




9 






6 


8 










5.3)t 


6 
6 
6 

5.6jt 


8.5 
7.0^ 


4.75< 




6.2ji 





In Table I are given the observed values of change in absorption 
due to frosting for the individual lamps of seven lots, obtained from 
different lamp factories and representing six different types of fila- 
ments, two of the lots having filaments of the oval-anchored type. 
As stated previously, the figures given represent the percentage 
decrease in mean spherical intensity due to frosting. The changes 
in mean horizontal intensity will be discussed later in connection 
with the changes in the distribution of the light due to frosting. 

In the first two columns are given the values for the two lots of 
oval-anchored filament lamps. Half of the lamps of Lot 2 were 
frosted by the acid process and half by the sand-blasting process. 
It is interesting to note the uniformity among the values of the 



98 Bulletin of the Bureau of Standards. [/ w. <, No. i. 

lamps of each kind, and the difference between the average absorp- 
tion coefficients for the acid-frosted and the sand-blasted lamps. 
The average value for the former is 3.8 per cent, with a range 
from 3 to 5 per cent for the individual lamps. For the latter the 
average is 5.6 per cent, with a range from 5 to 6 per cent. On the 
other hand, the average value for the lamps of Lot i, all of which 
were frosted by the acid process, is 5.3 per cent, which is nearer to 
the value for the sand-blasted lamps of Lot 2 than to that for the 
lamps frosted by the acid process. 

The only other lot of lamps of which parts were frosted by each 
of the two methods is Lot 3. Here again the acid-frosted lamps 
show a smaller absorption than the sand-blasted lamps, but the dif- 
ference is not as great as that obtained with the lamps of Lot 2. 
This is easily accounted for by the fact that the surfaces of the 
sand-blasted lamps of Lot 3 were of a much finer grain than those 
of Lot 2. It was difficult to separate the sand-blasted lamps of Lot 
3 from those frosted by the acid process. 

The total range in the average absorption coefficients for the 
acid-frosted and sand-blasted lamps of the seven different lots is 
from 3.8 per cent for the acid-frosted lamps of Lot 2 (oval-anchored 
lamps) to 7.5 per cent for the acid-frosted lamps of Lot 7 (down- 
ward-light lamps). The mean value for the seven different lots is 
5.7 per cent. 

The question arises whether the figures given in Table I are to 
be taken as indicative of the degree of uniformity to be expected in 
the frosting of lamps at different factories, and of the frosting of 
individual lamps at any one factory. Another pertinent question 
which might be raised is whether the average absorption coeflScient 
of 5.7 per cent which was found for lamps that had been seasoned 
applies equally well to new lamps. Since, in order to discuss fully 
the results on absorption in their bearing upon these questions it 
would be necessary to anticipate what will be said in regard to the 
change in life due to frosting, any further discussion of Table I will 
be deferred until the effect of frosting on life has been presented. 

Before passing to the next part of the paper, however, it is well 
to call attention to the probable errors of observation in making the 
measurements from which Table I was computed. An. error of i 
per cent in determining the mean spherical candlepower of an indi- 



^af] ^ Study of Plain and Frosted Lamps, 99 

vidual lamp either before or after frosting would make a difference 
of I per cent in the observed absorption coefficient, i. e., a lamp 
showing an apparent change in absorption of 4 per cent might in 
reality have undergone a change of 3 per cent or 5 per cent. If in 
each of the two determinations — ^before and after frosting — an error 
of I per cent had been made, it is possible that the observed change 
in absorption might be in error by 2 per cent, although this would 
be quite improbable. 

With the great number of observations to be made and the con- 
sequent speed with which they were conducted, it was impossible to 
give to each measurement the care requisite to obtain an accuracy 
better than i per cent. There is every reason to believe, however, 
that the observed average change in absorption is well within i per 
cent of the true value for those lamps. 

Attention is called to this question of probable error, in order that 
in considering this and subsequent tables too much weight may not 
be given to small differences in individual lamps. 

3. CHANGE IN DISTRIBUTION. 

A second important effect of frosting incandescent lamps is the 
change produced in the polar distribution curves of the lamps. It 
would seem at first thought, perhaps, that frosting the bulb of an 
incandescent lamp would produce a more uniform distribution of 
the light; in other words, the spherical reduction factor, i. e., the 
ratio of the mean spherical to the mean horizontal candlepower, 
would approach unity. Such, however, is not the case. The shape 
of the lamp bulb is an important determining factor. If we sup- 
posed the frosted bulb to act as a perfect mat surface, i. e., to trans- 
mit no light directly but to scatter or diffuse the light completely, 
and if we assumed the form of the filament such that the whole 
frosted surface of the bulb were unifonnly bright, then we could 
predict with reasonable certainty the approximate distribution of the 
light around the lamp. If the shape of the bulb were spherical, the 
intensity would be the same in all directions, and the reduction 
factor would be unity. If the bulb were a long, slender cylinder, 
the intensity would be a maximum in a direction normal to the axis 
of the cylinder, but would decrease as we approached the ends of 
the cylinder, the reduction factor being approximately 0.79. 



lOO 



Bulletin of the Bureau of Standards. 



[ / 'ol. /. So. I. 



In the actual case of frosted incandescent lamps the problem is 
not nearly so simple. The frosting is never so complete as to 
eliminate all direct transmission, and the shape of the bulb is not a 
simple geometrical figure, particularly if the effect of the base is 
considered. But the shape of the bulb has a marked influence on 
the distribution curve, as will be seen shortly from the experimental 
results. 

There are two ways of showing the effect of frosting on the 
distribution — (i) by comparing the spherical reduction factors 
before and after frosting, and (2) by actually plotting the distribu- 
tion curves of plain and frosted lamps. The second method is 
more satisfactory, but requires many more observations. We have 
used both methods. The average reduction factors for a number of 
lamps of each of the six different types of filaments described pre- 
viously were determined before and after frosting. The values 
obtained for the individual lamps of the various types will be given 
below (section 4). 

TABLE II. 

Average Reduction Factors and Absorption Coefficients for R^dar 

Lamps. 



Lots 



Ho. 1 (odd) 
Ho. 2 (add) 
Ho. 2 (sand) 
Ho. 3 (add) 
Ho. 3 (sand) 
Ho. 4 (add) 
Ho. 5 (add) 
Ho. 6 (add) 
Ho. 7 (add) 



Types of filament 



Reduction factors 



Absorption 
coefficients 



Plain 



Oval anchored 

Oval anchored , 

Oyal anchored 

Double filament 

Doable filament 

Spiral filament. 

Doable roand coil 

Doable flattened coil . 



0.826 
.824 
.828 
.806 
.809 
.914 
.884 
.972 
Downward Ugfat ' 1.064 



Frosted 



Mean 



Mean 
horixon- 



spherical; ""Ya* 



0.825 


5.35t 


5.05< 


.825 




4.0 


.825 




5.4 


.784 




3.7 


.797 




5.9 


.863 




-0.9 


.885 




5.0 


.984 




7.3 


1.027 




4.2 



In Table II the average reduction factors before and after frosting 
are given in the third and fourth columns. The reduction factor of 
the oval-anchored lamps is substantially the same before and after 
frosting, showing no tendency to approach unity. The change in 
the reduction /actor for all the other types of lamps is small except 



^5^;] A Study of Plain and Frosted Lamps, loi 

for the spiral-filament and downward-light lamps. The former 
shows a decrease in reduction factor of 5.5 per cent and the latter a 
decrease of 3.5 per cent — that is, the effect of frosting is to dimin- 
ish the mean spherical candlepower relatively more than the mean 
horizontal. This is also shown by a comparison of the spherical 
and horizontal absorption coefficients. In the fifth column the aver- 
age spherical absorption coefficients are copied from Table I. In 
the sixth column the changes in horizontal absorption are given. 
The large decrease in reduction factor for the spiral-filament lamps 
is shown here as an actual increase in mean horizontal candlepower 
due to frosting, whereas the decrease in mean spherical intensity 
on frosting is over 4.5 per cent. It is evident, therefore, that the 
changes in mean horizontal intensity are no criterion of the actual 
absorption due to frosting. 

A comparison of the spherical reduction factors before and after 
frosting, however, does not give a fair idea of the relative distribu- 
tion curves under the two conditions. Thus, although the ratio of 
mean spherical to mean horizontal intensity is not altered apprecia 
bly by frosting the oval-anchored filament lamps, the distribution of 
light in the two cases is not the same. Before discussing the rela- 
tive distribution curves (Figs. 5 to 13) of the plain and frosted bulb 
lamps of each of the six types of filament studied, some experiments 
made with lamps having special bulbs will be described. 

In order to show experimentally that the shape of the bulb is an 
important factor in determining the distribution of the light around 
frosted lamps, we obtained, through the courtesy of the General 
Electric Company, a number of regular oval-anchored filaments 
mounted in 3^-inch spherical bulbs, of which some were frosted. 
Subsequently we also obtained, through the kindness of the National 
Electric Lamp Association, a number of double-flattened coil and 
downward-light filaments mounted in the straight sides bulb SS-i 9, 
such as is commonly used with the oval-anchored filament, but 
which is not supplied with the regular double-flattened coil or 
downward-light lamp. 

These various special lamps were treated in the same way as the 
regular lamps, i. e., their spherical reduction factors and distribution 
curves were obtained. The average spherical reduction factors for 
each special type, both plain and frosted, are given in Table III. 



I02 Bulletin of the Bureau of Standards. \voi. 4, No. i. 

TABLE III. 
Average Reduction Factors for Special Lamps. 



Types of filament 


Shapes of bulb 


Reduction factors 


Plain 


Frosted 


Oval Anchored 


3^ in. round bulb 


0.840 
.982 
.995 


0.887 


Downward light 


Straijlit Bides 88-19 bulb 


.938 


Double-flattened coil 


Stiaic^t sidee 88-19 bulb 


.935 









In the study of the special lamps, four plain and seven frosted oval- 
anchored lamps were used, four plain and four frosted double- 
flattened coil lamps, and five plain and two frosted downward-light 
lamps. Owing to the small number of lamps studied, the precise 
numerical values obtained are not to be insisted upon, but the 
general conclusions drawn from the results would seem to be 
perfectly definite. 

The effect of the shape of the frosted bulb is evident at once in 
the difference between the reduction factors for the regular frosted 
and the special round-bulb frosted lamps with oval-anchored fila- 
ments. The value for the former is 0.825, that for the latter 0.887, 
a difference of over 7 per cent. Another striking illustration is 
afforded by the downward-light lamps. The average reduction 
factor for the regular frosted-bulb lamps is 1.027, whereas ^^ reduc- 
tion factors for two downward-light filaments mounted in SS-19 
frosted bulbs were found to be 0.935 and 0.94. The average value 
0.938 is almost 9 per cent different from the average value for the 
regular lamps. The differences in the shapes of the distribution 
curv^es will be discussed presently. 

Another interesting result, which also becomes clearer when we 
consider the distribution curves, is the change in the reduction factor 
of plain-bulb lamps with change in shape of bulb. Only a few 
lamps were studied and the numerical differences found are not very 
large, but we are quite certain that the shape of the bulb has an 
appreciable influence on the reduction factor and on the distribu- 
tion curve. Thus the average reduction factor for the four special 
round-bulb lamps is 0.840, whereas only one lamp of the forty-five 
regular-bulb lamps studied has a value that high, the average for 



c^\] A Study of Plain and Frosted Lamps. 103 

the forty-five lamps being 0.826. The effect is more noticeable with 
the downward-light lamps. The average reduction factor for the 
regular lamps is 1.064; ^^^ the five special lamps it is 0.99^, a differ- 
ence of almost 7 per cent. Moreover, the lowest value for any of the 
twenty-three regular lamps is higher than the highest value for any 
of the five special lamps. 

The differences both for the plain and the frosted lamps are 
clearer when we plot the distribution curves. In Figs. 5 and 6 are 
shown the average vertical distribution curves for the plain and the 
frosted double-filament and spiral-filament lamps — the two extreme 
types which are supplied with the ordinary straight sides bulb 
SS-19. In plotting all the curves the mean horizontal intensity is 
taken as unity. No attempt was made to determine the exact form 
of the curve in the neighborhood of the base, since it depends to 
such an extent upon the style of rotator used, the distance at which 
the measurements are made, etc. The measurement nearest the 
base was made at 165°, or 15° from the base. The intensity at the 
base was assumed to be zero. As stated previously, in determining 
the distribution curves the speed of rotation was 200-250 r. p. m. for 
all lamps except those having pronounced flickers at that speed. 
For these lamps higher speeds were used, so that the curves obtained 
may be slightly different from those that would be obtained at low 
speeds if it were possible to make accurate readings with a badly 
flickering illumination of the photometer screen. 

The two curves to the right in Fig. 5 are for the spiral-filament 
lamp, the solid curve applying to the plain-bulb lamp and the 
dotted curve to the frosted-bulb lamp. Similarly, the two curves to 
the left in Fig. 5 are for the plain and frosted bulb double-filament 
lamp. In Fig. 6 these same curves are reproduced in a different 
arrangement in order to compare the two plain-bulb curves and 
the two frosted-bulb curves. 

It is evident, first, from Fig. 5 that frosting modifies greatly the 
distribution curve of the plain lamps. In paf ticular, it is interesting 
to note that in the double-filament lamp the tip candlepower is 
increased relative to the mean horizontal intensity, whereas in the 
spiral-filament lamp it is decreased. From Fig. 6 it is seen that 
the curves of the two frosted lamps are more nearly alike than the 
curves of the two plain lamps, due to the fact that both types of 



I04 



Bulletin of the Bureau of Standards. \voi. /. no. t. 




i 






^^;] A Study of Plain and Frosted Lamps. 105 

filaments are in the same bulb, and the shape of the bulb impresses 
its character on the distribution curves of the frosted lamps. 

In Figs. 7 and 8 are shown similar curves for oval-anchored fila- 
ments in regular SS-19 and special round bulbs, plain and frosted. 
In Fig. 7 the two curves to the right are for the plain and frosted 
regular bulbs; the two to the left are for the plain and frosted special 
round bulbs. The effect of the shape of the frosted bulb is clearly 
evident from the two curves to the left in Fig. 8, of which the solid 
curve applies to the regular bulb and the dotted curve to the special 
round bulb, in both of which regular oval-anchored filaments were 
mounted. The two curves to the right in Fig. 8 show the effect 
of the shape of the plain bulb on the distribution cur\^e. 

This effect is more pronounced in the case of downward-light 
filaments mounted in their regular and in straight sides SS-19 bulbs, 
as shown by Figs. 9 and 10. These curves are analogous to those 
for the oval-anchored filament in Figs. 7 and 8. The effect of the 
shape of the bulb, both for the frosted and plain lamps, is quite 
noticeable. 

In Figs. II and 12 similar curves for double-flattened filaments 
mounted in their regular and in straight sides SS-19 bulbs are 
given. The same general effects are noticed with this type of fila- 
ment as with the oval-anchored and downward-light filaments. In 
Fig. 13 the distribution curves for the double round-coil filament in 
regular plain and frosted bulbs are shown. 

The curves given in Figs. 5-13 are the average vertical distribu- 
tion curves of the lamps, obtained by rotating each lamp about its 
axis of figure and determining the mean latitudinal intensity for 
different latitudes. A complete study of the effect of frosting would 
involve a determination of the distribution of light in each latitude. 
It would seem to us that too little significance is usually attached to 
the distribution of the light in space. In order properly to design 
fixtures for illuminating a room it is as necessary to know the dis- 
tribution of the light in any latitude as it is to know the average 
distribution in the vertical plane. 

4. SPHERICAL SEDUCTION FACTORS. 

It is generally recognized that the proper basis of comparison for 
lamps having different distribution curves is the ratio of the total 
flux of light eiilitted to the rate at which energy is supplied to the 



io6 



Bulletin of the Bureau of Standards. [^w. 4. Na i. 




^ 



i 






A Study of Plain and Frosted Lamps. 



107 




bo 



bo 



io8 



Bulletin of the Bureau of Standards, 



lVoh4.No.j. 







bo 



^g^;] A Study of Plain and Frosted Lamps. 109 

lamp. This involves a determination of the total flux of light, or, 
more commonly, of the mean spherical candlepower of the lamp. 
Although various types of integrating photometers for determining 
the mean spherical candlepower of incandescent lamps have been 
devised — ^some of them very excellent for laboratory purposes — there 
has never been developed such a photometer which could be in- 

DOUBLE ROUND COIL FILAMENTS 
REGULAR BULBS 




PLAIN . 

FROSTED 

stalled and used with satisfaction in a, lamp factory- . As a result, 
very few lamps have been purchased heretofore in the United States 
on this basis. Until an integrating photometer suitable for use in 
lamp factories and testing stations is placed on the market the mean 
spherical rating can best be accomplished by the use of spherical 
reduction factors. This method has been incorporated in the lamp 
8919 — 07 8 



no 



Bulletin of the Bureau of Standards. 



[ Vol^ /, So. I. 



specifications recently adopted for use by most of the departments 
of the Government. 

The idea of the spherical reduction factor is an old one, and it 
has long been known that for any type of incandescent lamp the 
spherical reduction factor is approximately constant for individual 
lamps of that type. Many investigations of the values of spherical 
reduction factors for diJBFerent types of incandescent lamps have been 
published, but owing to the recent renewed interest in the question, 
and the improved facilities at our disposal for measuring mean 
spherical candlepower, it seemed desirable to include in this investi- 
gation on the eflFect of frosting an auxiliary study of the spherical 
reduction factors of the six types of lamps used. 



TABLE IV. 
Spherical Reduction Factors of Regular Plain Bulb Tramps. 



Oval anchored 


Double fila- 
ment 
Lota 


Spiral fila. 
ment 
Lot 4 


Double 

round coil 

Lots 


Double flat- 
tened coil 
Lot 6 


Downward 
light 
Lot 7 


Lot X 


Lota 


0.82 


0.81 


0.80 


0.89 


0.87 


0.97 


1.04 


.82 


.81 


.80 


.90 




87 


.97 


1.04 


.82 


.82 


.80 


.90 




87 


.97 


1.04 


.82 


.82 


.80 


.90 




88 


.97 


1.04 


.82 


.82 


.80 


.90 




88 


.97 


1.04 


.82 


.82 


.80 


.90 




88 


.97 


1.Q5 


.82 


.82 


.80 


.90 




88 


.97 


1.05 


.82 


.82 


.80 


.91 




88 


.97 


1.06 


.82 


.83 


.80 


.91 




88 


.97 


1.06 


82 


.83 


.81 


.91 




88 


.97 


1.06 


.82 


.83 


.81 


.91 




88 


.97 


1.06 


.83 


.83 


.81 


.91 




88 


.97 


1.07 


.83 


.83 


.81 


.91 




88 


.97 


1.07 


.83 


.83 


.81 


.91 




89 


.97 


1.07 


.83 


.83 


.81 


.91 




89 


.97 


1.07 


.83 


.83 


.81 


.91 




89 


.97 


1.07 


.83 


.83 


.81 


.92 




89 


.97 


1.07 


.83 


.83 


.81 


.92 




90 


.97 


1.06 


.83 


.83 


.81 


.92 




90 


.97 


1.06 


.83 


.83 


.81 


.92 




90 


.98 


1.06 


.83 


.83 


.81 


.92 




.98 


1.06 


.83 


.83 




.93 




.96 


1.09 




.84 




.93 
.93 
.93 * 




.96 
.96 


1.09 


0.825 


0.827 


0.806 


0.912 


0.884 


0.972 


1.063 



^^;] A Study of Plain and Frosted Lamps, 1 1 1 

In Table IV are given the results obtained on the individual 
lamps of each type before they are frosted/ 

It is seen that for forty-five lamps of the oval-anchored type 
obtained from two different manufacturers the total range is from 
0.81 to 0.84, the greatest observed deviation from the mean being 
less than 2 per cent. The agreement among the observed values 
for lamps of the double-filament type (IvOt 3) and for those of the 
double flattened-coil type (IvOt 6) is even better. The largest diflFer- 
ences were observed with lamps of the downward-light type (IvOt 7), 
where a maximum deviation from the mean of about 2.5 per cent was 
found. One would expect the variations among lamps of this type 
of filament to be larger than those among lamps of other types, 
because of the relatively rapid change in intensity in the neighbor- 
hood of the horizontal for downward-light filaments. 

But when we contrast the 2 or 2.5 per cent maximum deviations 
of individual lamps of any one type from the mean value for the 
type with the 20 or 30 per cent differences between the various 
mean values for the different types, it is apparent that in the absence 
of a cheap, convenient, and accurate photometer for measuring mean 
spherical candlepower directly, the spherical-reduction factor oflFers 
an excellent substitute in the commercial rating of lamps on the 
basis of mean spherical efficiency. 

5. CHAIfGB IN LIFE. 

It has long been recognized that the useful life of a frosted incan- 
descent lamp taken to 80 per cent of its initial mean horizontal 
candlepower is only a little more than one-half of the life of a corre- 
sponding plain-bulb lamp. The only explanation which had been 
advanced, so far as the authors know, previous to that suggested by 
the present investigation is that the temperature of the frosted lamp 
is higher, due to the increased absorption by the bulb, and that 
therefore the lamp reaches any given point in its life— e. g., the 80 
per cent point — in a shorter time than that required for the corre- 
sponding plain-bulb lamp. 

•The slight decrepancies between values given in Table II and those given in Table 
IV are due to the omission of the figures in the third decimal place in the values of 
the individual lamps in Table IV. These were taken into account in computing the 
means given in Table II. 



112 Bulletin of the Bureau of Standards, [ voi, /, No. i. 

Without entering at present into a discussion of the possible tem- 
perature effects, it is sufficient to notice that if the shortened useful 
life can be attributed to this cause, it is ver^' probable that, due to the 
same cause, the total life of a frosted lamp up to the time when the 
filament burns out would also be very much less than that for the 
plain lamp. On the contrary, tests carried out at the laboratories of 
the National Electric Lamp Company by Mr. S. E. Doane indicated 
that the average total life of frosted lamps is not very different from 
that of corresponding plain lamps. It would seem, therefore, that 
some explanation other than that of the effect of temperature must 
be sought. A possible explanation of the phenomenon occurred to 
one of the authors in the course of the present investigation. An 
experiment devised to test it showed conclusively that it would 
account for at least a large part of the effect, if not for all of it. 
This explanation, together with a brief account of the preliminary 
experiments supporting it, was published in the Electrical Review* 
several months ago. 

The explanation, as outlined in that paper, from which we quote, 
is as follows: "If we consider the case of a new plain-bulb lamp, a 
certain small percentage of the total flux of light emitted by the 
incandescent filament is absorbed by the glass envelope surrounding 
the filament. When the lamp is frosted a large part of the light 
which in the plain bulb would pass through the outer surface of the 
bulb is diffusely reflected back through the glass. In this way a 
relatively large part of the total flux of light passes through the 
glass more than once, and so the frosted bulbs show an absorption 
about 5 per cent greater than that for the plain bulbs. 

Now, the actual absorption coefficient of glass is quite small, so 
that it is readily seen that if in any way the absorption coefficient is 
increased appreciably, the apparent absorption due to frosting would 
be increased greatly. This is what happens when with increasing 
life the strongly absorbing film is deposited on the inside of the 
bulb. The effect is the same as if the absorption coefficient of the 
glass had been increased greatly." In the case of an old plain lamp 
all the light passes through the carbon film once, a small percentage 
passes through three times, a still smaller percentage five times, and 

® Electrical Review, April 6, 1907; p. 556. See also this Bulletin, 3, p. 341; 1907. 



^ 



c^[] ^ Study of Plain and Frosted Lamps. 113 

so on. When the lamp is frosted the percentage of light that passes 
through more than once is very much larger, so that the carbon film 
has an opportunity to absorb a much larger percentage of the total 
flux. According to this theory, although at any time the filament 
in the frosted bulb may be emitting the same total flux of light as 
that emitted by the filament in the plain bulb, the absorption of 
light in the carbon film is much greater in the one case than in the 
other, and so the apparent intensity of the frosted lamp at any time 
during life is less than that of the plain lamp, the difference in 
intensity increasing with the number of hours the lamps have burned. 
In order to make a quantitative determination of this effect, after 
convincing ourselves by a few qualitative experiments that the effect 
was a real one, ten comparatively new lamps and twelve old lamps that 
had dropped to 80 per cent in candlepower were carefully measured 
for mean horizontal and mean spherical intensity. They were then 
sent to a lamp factory and frosted by the acid process, care being 
exercised to see that the frosting was as nearly uniform for the dif- 
ferent lamps as it was possible to obtain. The lamps were then 
returned to the Bureau of Standards and measured. The new lamps 
were found to have decreased in mean horizontal intensity by about 
4 per cent on the average, the individual lamps agreeing among 
themselves to within less than 2 per cent. On the other hand, the 
older lamps decreased in mean horizontal intensity by 18 per cent, 
or 14 per cent more than the new lamps. In other words, the appar- 
ent absorption of the frosting was approximately four and one-half 
times as great for the old lamps as for the new lamps. This means 
that if we were to assume no difference in the physical or mechanical 
properties of plain and frosted lamps, a lot of plain lamps which 
would decrease 20 per cent in candlepower in a definite number of 
hours would in the same number of hours decrease approximately 
32 per cent if they were first frosted. The useful life of the frosted 
lamps to 80 per cent of initial candlepower would be about 60 or 70 
per cent of the useful life of the plain lamps, a value in approxi- 
mate agreement with that commonly accepted. This shows that 
whatever effects may be produced in the lamps by frosting them, the 
mere absorption by the deposited carbon film, as explained above, is 
sufficient to account for a decrease in useful life of about 30 or 40 
per cent. 



114 Bulletin of the Bureau of Standards, \vol /, No. i. 

The new lamps decreased about the same in mean spherical as in 
mean horizontal candlepower, whereas the old lamps decreased sev- 
eral per cent more in mean spherical intensity. This is probably 
due to the uneven distribution of carbon on the inside of the bulb. 

Several weeks after the above explanation was printed in the 
Electrical Review, Mr. Preston S. Millar published in the Electrical 
World *° an account of some experiments made upon frosted lamps 
at the Electrical Testing Laboratories. It is very interesting to 
note that the results of Mr. Millar's experiments are in very good 
agreement with those obtained at the Bureau of Standards and fur- 
ther substantiate the theory outlined above. Quite recently Dr. A. 
E. Kennelly has put this theory into a mathematical form in a 
paper published in the Electrical World." 

In the preliminary paper printed in the Electrical Review an 
experiment was outlined to detennine whether there are any other 
elements entering to bring about the short useful life of frosted 
lamps. This experiment has just been completed. Out of a num- 
ber of iio-volt, i6-cp, 3.1-wpc oval-anchored filament lamps five 
lots of twenty-two lamps each were selected and designated as Lots 
A, B, C, D, and E. The nearest even voltage for each lamp was 
found corresponding to an initial specific consumption of j^,j^ watts 
per mean horizontal candle. In all the subsequent photometric 
measurements the lamps were burned at these voltages. On the life 
rack, however, in order to hasten the completion of the investigation, 
the lamps were maintained at a voltage 12 volts higher than that at 
which they were measured on the photometer. This voltage corre- 
sponded to an initial specific consumption of approximately 2.3 watts 
per mean horizontal candle. 

The five lots of lamps were measured carefully for initial mean 
horizontal candlepower, and then all the lamps except those of Lot 
A were placed on the life rack. The lamps of Lot B were burned 
for 9 hours, those of Lot C for 37 hours, and those of Lots D and E 
for 78 hours, at which time it was expected that the lamps would 
have reached the 80 per cent point. On measuring all the lamps 
for mean horizontal candlepower it was found, however, that the D 

*^ Electrical World, April 20, 1907; p. 798. 
"Electrical World, May 18, 1907; p. 987. 



Chdy.A 



A Study of Plain and Frosted Lamps. 



115 



and E lamps had only decreased in candlepower to 83 per cent of 
the initial value. 

All the lamps with the exception of those of Lot E were then sent 
to the factory to be frosted. Upon their return they were all meas- 
ured again for mean horizontal candlepower and placed upon the 
life rack, with the exception of those of IvOt D, which already had 
burned for 78 hours and had decreased in candlepower (before being 
frosted) to 83 per cent of their average initial value. The lamps of 
each of the three Lots A, B and C were burned the requisite num- 
ber of hours to make the total time of burning 78 hours. 

In this way all the lamps were made to bum 78 hours, but the 
paths followed by the various lots were different. Thus, Lot A 
burned the total 78 hours after having been frosted; Lot B burned 9 
hours while plain and 69 hours after having been frosted; Lot C 
burned 37 hours plain and 41 hours frosted, and Lot D burned the 
entire 78 hours before being frosted. The average candlepowers of 
each lot at the various stages are given in Table V. In the first 

TABLE V. 

A Comparative Study of the Changes in Candlepower of Plain and Frosted 

Tramps During Life. 





Mean horizontal candlepower 


Mean spherical 
candlepower 




A 


B 


C 


D 


E 


A 


D 


fPtoin 


15.31 
100< 

S 

86 
72 


15.29 
1005< 

99 

85 
72 


15.15 
lOOjt 

94 
87 

73 


15.26 
1005< 

83 

n 


15.29 
100)< 

83 


12.61 
1005< 
96 

70 


12.62 

loojt 


•'"f.o.w 






""fHI*::::::::::::::::: 




fPtoin , . 




37 1ix»«„_^ 

bVmWH 

fPUii. . 


82 


"'"f.o.w 


70 






HorixoBtilA'btoiptioii oooffldcnt. 


1(0 hlB) 


(91118) 


(37 hn) 


Hi 

(78hlB) 









column are given the different times at which photometric measure- 
ments were made, together with a statement of the condition of the 
lamps at that time, whether plain or frosted. In the next five 



1 16 Bulletin of the Bureau of Standards. \voi. 4, no. i. 

columns are given the average mean horizontal candlepowers of the 
five different lots at the various stages of their life. In the first 
line the actual average candlepower of each lot is g^ven, but in the 
succeeding lines the candlepowers are expressed in per cents of the 
initial value of each lot. The average candlepower of each lot 
determined immediately after the lamps were returned from being 
frosted is underscored, so that it is easy to see how many hours each 
lot burned before and after having been frosted. 

It is interesting to note the marked agreement among the differ- 
ent lots upon reaching the same point in the cur\'e by different 
paths. Thus, after 37 hours Lot A had decreased to 86 per cent, 
Lot B to 85 per cent, and Lot C (frosted) to 87 per cent, although 
the A lamps were frosted initially, the B lamps after 9 hours, and the 
the C lamps after the entire ^j hours burning. Again, at the end 
of 78 hours the four lots A, B, C, and D had decreased in candle- 
power to the same value within about i per cent, although the A 
lamps burned the entire 78 hours after frosting, whereas the D 
lamps were frosted at the end of the 78 hours, the other two lots 
having been frosted at intermediate points. In other words, these 
tests would seem to indicate that the frosting has no appreciable 
effect upon the life curve of the filament, the short, useful life of 
frosted lamps being due entirely to the increased absorption of the 
light by the deposited carbon film, as explained above. 

Mr. Millar, in the paper referred to previously, described one set 
of experiments in which the candlepower of some frosted lamps 
which had burned a number of hours and which were soiled, 
increased by about 10 per cent upon being washed. One can 
readily see how the candlepower of frosted lamps could be changed 
considerably by the presence of dirt on the surface. In order to see 
whether this element played any part in the investigation at the 
Bureau, three of the A lamps which had burned 155 hours were 
measured for mean spherical candlepower before and after being 
washed. The increase in candlepower after the lamps were cleaned 
was about i per cent on the average. Since these three lamps had 
been exposed double the time used in the test, the effect of dust on 
the bulbs was evidently entirely negligible. 

Upon completing the candlepower measurements after 78 hours, 
all of the frosted lamps, and, in addition, the lamps of Lot E, which 



cadv^ ^ Study of Plain and Frosted Lamps, 117 

had burned to 78 hours, but which had not been frosted, were 
placed on the life rack and kept burning, in order to see whether 
there is any indication of an efFect of frosting on the total life of the 
lamps. The average total life of the lamps of each group until 
they burned out is as follows: Lot A, 104 hours; Lot B, 118 hours; 
Lo^ C, 133 hours; Lot D, 123 hours; Lot E, 118 hours. If frost- 
ing played an important part in determining the actual life of the 
filaments, the average total life of each successive group, in the 
order of the letters of the alphabet, would be greater than the pre- 
ceding. There is no indication, however, of such a sequence. It 
is true that the life of the A lamps is the shortest, but the life of 
the E lamps, which should be the longest, is no greater than that 
of the B or D lamps, and is much less than that of the C lamps, 
which burned nearly three-fourths of their life after having been 
frosted. It is evident, therefore, that this test shows no marked 
effect of frosting on the life of the filament. 

As shown in the last two columns of the table, the two extreme 
lots A and D were measured also for mean spherical candlepower. 
Here, as in the mean horizontal measurements, the average candle- 
power of the frosted lamps after 78 hours burning is the same, 
independent of whether the lamps are frosted first and burned 
subsequently, or vice versa. The decrease in mean spherical can- 
dlepower, however, is slightly greater than the change in mean 
horizontal intensity. This agrees with the results given in Table V. 

In discussing the change in absorption due to frosting, the ques- 
tion was raised as to whether the absorption of new lamps is the 
same as that of seasoned lamps. The answer to this is evident from 
a consideration of Table V. The change in horizontal candlepower 
due to frosting is given in the last line of the table. The A lamps, 
which were frosted when new, showed an absorption of 2 per cent ; 
the B lamps, frosted after 9 hours, an absorption of 4 per cent ; the 
C lamps, after 37 hours, an absorption of 7 per cent; and the D lamps, 
after 78 hours, an absorption of 12 per cent. The average value of 
5.7 per cent given earlier in the paper for seasoned lamps is there- 
fore probably several per cent higher than the correct value for new 
lamps. 

Since, in seasoning the lamps which were used in studying the 
change in absorption due to frosting, no special care was exercised 



1 18 Bulletin of the Bureau of Standards, \,voi. 4, No. /. 

to see that they all burned at the same temperature for the same 
number of hours, it is not at all surprising that differences in absorp- 
tion coefficients among different makes, or even among the indi\dd- 
ual lamps of any one make, occurred, since the carbon deposits may 
have been different. 

Having shown that for the lamps studied at the Bureau and for 
the conditions under which the investigation was made the short- 
ened life of frosted lamps can be accounted for entirely by the 
increased absorption of light by the carbon film deposited on the 
inner side of the bulb, it is interesting to consider briefly the ques- 
tion of temperature effects due to frosting. It would be very diffi- 
cult to determine the temperature of the incandescent filament 
before and after frosting the bulb by an optical method because of 
the complications arising from the frosted surface. An attempt was 
made to determine the change of temperature of the filament by 
measuring the change in resistance of the filament; but though this 
method gave definite indications in some cases, the results were not 
consistent. It is probable, however, that using filaments with larger 
temperature coefficients and taking extra precautions in the measure- 
ments, consistent results could be obtained with this method. 

Although no direct measurements of the temperature of the fila- 
ment were made, Mr. H. C. Dickinson, of the Division of Thermome- 
try, kindly undertook to determine the temperature of the bulbs of 
several of the A and D lamps at different periods in their life. By 
the use of a platinum resistance thermometer, placed around the 
bulb and in contact with it on the circumference of the circle of 
maximum diameter, the values given in Table VI were obtained. 

The actual rise in temperature on lighting the lamp, as measured 
by this method, may not be correct to a high accuracy, but the error 
is small. The relative temperature changes at the different periods 
in the life of the lamps are more nearly correct. 

It is seen from Table VI that the temperatures of the bulbs of 
new plain lamps are about ^j^ above room temperature. When a 
new lamp is frosted the temperature of the bulb increases by about 
9°. When a lamp is burned to about 83 per cent in life, the tem- 
perature of the bulb rises only 3° due to the carbon deposit, but 
when an old lamp is frosted the rise due to frosting is about 15°. 



S^:] 



A Study of Plain and Frosted Lamps. 
TABLE VI. 



119 



A Comparative Study of the Changes in Temperature of the Bulbs of Plain 
and Frosted Lamps during Life. 



Lamps 


Time 


Temperatures (cen- 
tigrade) 


Average 
rise above 




Of bulb 


Of room 


perature. 


A-1 Plain 


OhiB 

o«« 

OhiB 

0** 

78hlB 

78** 

78** 

OhiB 
0** 

78hi8 
78'* 

7811TB 
78** 


60° 
60° 
60° 

71° 
69° 
69° 

78° 
83° 
78° 

58° 
60° 

59° 
63° 

75° 
78° 


22° 
22° 
22° 

23° 
23° 
23° 

21° 
21° 
21° 

23° 
23° 

22° 
22° 

22° 
23° 




A-2 ** 


38° 


A-3 ** 




A-1 FiwtDd 




A-2 *' 


47° 


A-3 " ,-.. 




A-1 Frosted 




A-2 * * 


59^ 


A-3 ** 




D-1 Plain 




D-2 ** 


36° 


D-1 Plain 




D-2 " 


39P 


D-1 Frostod 




D-2 " 


54° 







Of course the energy supplied to the old lamps is 4 or 5 per cent 
less than that supplied to the new lamps. 

With the great difFerence in temperature between the filament and 
the bulb, the small variations in the temperature of the latter would 
scarcely be expected to change the temperature of the filament appre- 
ciably, so that although it is true that the bulbs of frosted lamps are 
hotter than those of plain lamps, the change in the temperature of 
the filament would probably not be noticeable in the life. 

It is very interesting, in conclusion, to follow out the practical 
results suggested by an investigation of this kind. For example, 
it is at once evident that the useful life of frosted lamps containing 
filaments of some material that would deposit no absorbing film on 
the inner side of the bulb, would be as great as that for the corre- 
sponding plain lamps, and the efficiency would only be a few per cent 
less. Experiments on metal filament lamps similar to those on lamps 
with carbon filaments will be made to determine the effect of frosting 
on the life of the former. 



I20 Bulletin of the Bureau of Standards. \voi. 4, jvo. i. 

The question of the most satisfactory size and shape of plain and 
frosted lamps is also very suggestive. For example, if the surfaces 
of bulbs of frosted lamps were doubled the useful life would be very 
much longer than at present. Another question of some importance 
in view of the present practice of using half-frosted lamps with 
reflector shades, is the extent to which the intensity of half-frosted 
lamps is diminished at different stages of their life. In other words, 
how does the useful life of a half-frosted lamp compare with that of 
a plain lamp? We hope to obtain some data on this question shortly. 

Washington, July 15, 1907. 



THE VARIATION OF RESISTANCES WITH ATMOSPHERIC 

HUMIDITY.^ 



By E. B. Rosa and H. D. Babcock. 



It has long been known that manganin resistances prepared in the 
manner developed by the Physikalisch-Technische Reichsanstalt do 
not remain entirely constant in value, but that appreciable differences 
sometimes occur among a group of apparently exactly similar coils. 
These variations are usually very small or inappreciable with coils of 
O.I ohm and i.o ohm; but with coils of lo, loo, i,ooo ohms and 
higher values the variations are often so considerable that when 
used for precision work it has been found necessarj^ at the Bureau 
of Standards to detennine their values by stepping up frequently 
from the i-ohm standards. These variations have been found to 
be greater in England than in Germany, and it has been sug- 
gested that the difference may be due to some difference in the 
methods of preparation of the coils followed in England and in 
Germany.* At the Bureau of Standards the variations in the values 
of manganin resistances have been a source of great annoyance, and 
they have been found to be as great in the resistances made by the 
best German makers as in those made in America. These varia- 
tions occur in the most carefully prepared standards of the Reich- 
sanstalt form, as well as in the resistances of Wheatstone bridges, 
potentiometers, resistance boxes, etc. 

SEASONAL CHANGES OF RESISTANCE. 

In the course of an extended investigation' at the Bureau of 
Standards on the ratio of the electromagnetic to the electrostatic 
unit of electricity it was found that all the resistances employed 

' Paper read before the American Physical Society at Washington, April 21, 1907. 
A preliminary account of this work appeared in the Electrical World of June 29, 
1907, and in the London Electrician, June 14, 1907. 

* Report of Prof. R. T. Glazebrook, Director of the National Physical Laboratory, 
Engineering (London), March 22 and April 5, 1907. 

•By E. B. Rosa and N. E. Dorsey; this Bulletin, 8, p. 433, 1907. 

121 



122 Bulletin of the Bureau of Standards. \voi. 4. no. i. 

had a higher value at the same temperature in summer than in 
winter, the change being a gradual drift upward from early spring 
to midsummer, followed by a steady drift back to the same mini- 
mum in the winter. The amplitude of the change was of course 
small, varying from 15 to 25 parts in 100,000, but was far too large 
to be neglected in precision work. Most of these resistances were 
kept submerged in oil all the time, but some were in air. In all 
cases the temperatures were taken and the resistance measurements 
made with great care. 

The possibility of these changes being due to atmospheric 
humidity suggested itself, but it was not at first evident how an 
increase of resistance could be produced by an increase of humidity. 
The effect of leakage arising from moisture deposited on the coils 
or upon the tops of resistance boxes is of course to decrease the 
resistance, and this effect would increase with the humidity. In 
order to ascertain the cause of the marked change in the opposite 
direction, to determine its magnitude, and to find how to prevent it, 
we took up last November a systematic study of the question. 

It was very soon found that changes such as occurred during an 
interval of six months in the atmosphere of the laborator>^ could be 
induced in a few days by placing the resistances in a closed case in 
which an atmosphere of high humidity was maintained, although 
it usually requir-ed several weeks for the resistance of a coil to reach 
a maximum, or to return to its former value when restored to the 
original conditions of humidity. 

Two apparatus cases were employed, the atmosphere within one 
being kept at a nearly constant relative humidity of about 25 per 
cent, the other being kept at higher humidities, ranging from 40 to . 
1 00 .per cent, although seldom higher than 80, and oftenest about 60 
per cent. Each case was provided with thermometers and record- 
ing hygrometers, the latter being frequently calibrated by aspiration 
psychrometers. 

The lower humidities were maintained by keeping calcium 
chloride in the apparatus cases, varying the quantity exposed 
according to the humidity desired. The higher humidities were 
obtained by exposing a greater or less surface of water in open ves- 
sels, and running a very small electric fan to circulate the air within 
the case. The records of humidities and temperatures were taken 
continuously through twenty-four hours, and comparatively small 



^S^ifc.] Variation of Resistances with Humidity. 123 

fluctuations occurred except those produced by intentional changes 
of the conditions. 

The higher resistances were measured generally to one or two 
parts in a million, and corrections made for small fluctuations in 
temperature. All measurements were finally referred to the standard 
of the Bureau determined by the mean value of a number of one-ohm 
and tenth-ohm coils. The changes in the resistances of the latter 
are known to be relatively small. 

CHANGES ARE DUS TO HOISTUSE ABSORBED BY SHELLAC. 

The cause of the increase in resistance of the manganin coils, the 
wire of which is embedded in a heavy covering of shellac thoroughly 
dried out by baking, is that the shellac absorbs moisture from the 
surrounding atmosphere and expands^ stretching the manganin 
wire and thereby increasing its resistance. The amount of moist- 
ure absorbed depends on the relative humidity of the atmosphere, 
the moisture in the shellac gradually coming to equilibrium with 
the moisture outside when any given humidity is maintained con- 
stant. When the atmosphere is drier the shellac gives up moisture 
and shrinks, and the wire also contracts and its resistance decreases. 
The resistance therefore is constantly changing with changes in 
atmospheric humidity, and is a constant only when the atmospheric 
humidity is constant or when the coil is sealed so that moisture 
can not get into the shellac. Dipping the coils in melted paraffin 
will seal them effectually against moisture, so that even the finest 
wire, such as is used in coils of 1,000 and 10,000 ohms, remains of 
constant resistance. Sealing such a coil in a test tube will keep its 
resistance constant, even though it had previously been exposed to 
a moist atmosphere. Submerging the coils in oil does not protect 
the shellac from atmospheric humidity^ as the oil absorbs moisture 
and transmits it to the coils. Hence submerged coils increase in 
resistance when the atmospheric humidity increases, and decrease 
in resistance when the humidity decreases. The oil retards the 
change of resistance and decreases the amplitude somewhat, but still 
permits considerable changes to occur, especially in the higher 
resistances. 

A change of resistance of 25 parts in 100,000 will be produced by 
an increase in length of the wire of 12.5 parts in 100,000. If the 
wire is wound on a spool 4 cm in diameter (the size used in a Wolff 



124 Bulletin of the Bureau of Standards, \voi. 4, No. i, 

standard of the Reichsanstalt form) the diameter must be increased 
by the swelling of the shellac by 0.0005 ^^ ^^ 5 inicrons. This is 
of course an appreciable increase in diameter, although much more 
difficult to measure than the change in resistance. Coils sealed by 
a covering of paraffin will remain constant for months through wide 
fluctuations of moisture, certainly to within a few parts in a million, 
which indicates that the diameter has not changed during that time 
by as much as 0.2/i, if at all. We shall presently give evidence to 
show that manganin wire of all sizes is remarkably constant in 
resistance, and that changes that have been attributed to the man- 
ganin are due to the shellac in which it is embedded. 

In Fig. I are given curves showing the seasonal changes of cer- 
tain resistances during the past two years. These cur\''es, which 
were plotted by Dr. Dorsey in the investigation referred to, prompted 
this study of the variation of resistances with humidity. The curv-es 
showed conclusively, what had probably never before been suspected, 
that the resistance of a shellac-covered manganin coil is greater in 
summer, at a given temperature, than in winter, at least under some 
conditions. These resistances were exposed only to the atmosphere 
of the laboratory, and in summer the humidity was kept lower than 
normal during 6 or 8 hours of nearly every working day by means 
of cold brine coils in the room, which condensed moisture upon 
them. The object of thus reducing the humidity was to secure 
more perfect insulation than could be obtained otherwise. This is 
especially necessary in the measurement of small capacities, where 
large resistances are employed and slight leakage is serious. The 
changes in resistances were therefore appreciably less than would 
have occurred normally. All resistance measurements were made in 
an atmosphere dry enough to give thoroughly satisfactory insulation. 

It is possible that the greater changes obser\^ed in England than 
in Germany in manganin coils that have been shellacked are due to 
greater ranges in the atmospheric humidity in England. That some 
English makers have reported no appreciable changes in their man- 
ganin resistances is probably explained by their use of paraffin for 
insulation instead of shellac. 

Fig. 2 shows the changes in certain manganin resistances when 
subjected to variations in atmospheric humidity, the values of the 
humidity, the dates and the variations in resistance being shown in 



Rosa. n 
BabcocM.J 



Variation of Resistances with Humidity. 



125 



WEPRESEWTa A CHANOE OF 1 IN 10,000 |W THE REfliaTANCE. 




126 



Bulletin of the Bureau of Standards. \yoi. 4. ao. a 



^ 


\ 




1 SQUARE 


REPRESENTS A CHANGE OF 1 IN 10,000 IN RESISTANCE. 






I* 

10 


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Fig. 2. — Changes pf resistance due to atmo^heric humidity. 
(For explanation of curves see opposite page.) 



BtS^^ V^^i^iion of Resistances with Humidity, 127 

the ciirves. The loooohm coil represented by curve 13 was first 
placed for a few days in a saturated atmosphere. The change in 
resistance was very rapid, but was suddenly stopped by reducing the 
humidity to 30 per cent A sudden drop in resistance followed, 
the rate of decrease being reduced by raising the humidity for a few 
days to 40 per cent. The rate of decrease was again augmented by 
reducing the humidity to 20 per cent. After the resistance had 
decreased to a point below its initial value, the humidity was 
increased to 55 per cent, when the resistance rose as shown and 
then fell when the humidity was reduced to 40 per cent The 
change in resistance between the maximum value of November 22 
and the minimum value of December 7 was 40 parts in 100,000. 
On January 2 a quantity of calcium chloride was placed in the bot- 
tom of the resistance box, which was closed up as nearly air-tight 
as practicable without sealing. The resistance fell rapidly for a few 
days (about 15 parts in 100,000) and then remained nearly constant 
for three months, but was not entirely independent of changes in 
room humidity. The higher average humidity of April caused the 
resistance to rise appreciably. 

Curves 17 and 19 show how closely the 1000 coil and the Siooo 
(made up of coils of 500+ 200+ 100+ 100+ 2ioo) vary together as 
the humidity is varied. In this case also CaCl, was added to the 
box on January 2, resulting in a decrease in resistance. When the 
box was placed in an atmosphere of 60 and 70 per cent humidity 
the resistance rose appreciably in spite of the CaCl,. After the 
calcium chloride was removed the box was put in the damp case 
and the resistances rose rapidly, and then decreased when the 
humidity was reduced to 40 per cent, and then increased again with 
a humidity of 60 per cent. 



Explanation of curves of Fig. ^, p. 126. 

The curves of Fig. 2 show variations in manganin resistances due to changes in 
atmospheric humidity. Resistances kept in an inclosed space where the humidity 
was under control. Observations extended through eight months. The relative 
humidities are indicated on the curves. One vertical space is i part in 10,000 in 
resistance. 

Curve 13 is 1,000-ohm coil in air from Wolff box No. 3087. (Same coil as No. 3 
of Fig. I. ) Curve 17 is i,ooo-ohm coil in air from Wolff box No. 3080. Curve 19 is 
Zi,ooo-ohm coil in air from Wolff box No. 3080. Curve 27 is 1,000-ohm coil in air 
made by the Leeds and Northrup Company. 



128 



Bulletin of the Bureau of Standards, 



\VoL4.No.i. 




1907 



TT S 51 re- 
Fig. 3. — ChcmgBs of resistance of coils. 



The curves of Fig. 3 show changes in resistance of manganin coils of 10 and 100 
ohms. 

Curves i8a and i8b are two coils of 100 ohms each in air, Wolff box No. 3080. 
Curves 20a and 20b are two coils of 10 ohms each in air, Wolfif box No. 3080. 



BadcocA.J 



Variation of Resistances with Humidity, 



129 



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* 1 SQUARE REPRESENTS A CHANGE OF \ W 10,000 IN RESISTANCE. 


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130 Bulletin of the Bureau of Standards, ivta. 4, No. /. 

Curve 27 represents a shellacked manganin coil made by the 
Leeds and Northrup Company, showing large changes in resistance 
as the humidity is varied. 

Fig. 3 shows that the changes in coils of heavier wire, as used in 
resistances of 10 and 100 ohms, are very considerable, amounting to 
35 to 50 parts in 100,000, due to 80 per cent humidity. 

Fig. 4 shows three resistances from Wolff box No. 2471 (all in 
oil), which have been kept for several months at as nearly constant 
humidity as possible and which have remained remarkably constant 
in value. Curve i represents the same set of coils (2 1,000) as curve 
5 of Fig. I. During November and December it gradually decreased 
in value, coming to an equilibrium value for approximately 25 per 
cent humidity about January i. Between January i and July 9 
this coil changed only a few parts in 1,000,000, having come down 
to a minimum value in March. The average humidity in the case 
has been a little higher since March, and this probably accounts for 
the slight increase in resistance. Curve 5 represents a single spool 
coil of 10,000 ohms, and curve 3 represents the 2io,ooo coils of the 
same box. These three curves are practically horizontal, all showing 
a minimum in March a few parts in a million less than the values in 
January and since April, the drop in January and February being 
doubtless due, as stated above, to the continued drying out of the 
oil, and the rise in April to a slightly higher humidity in the case, 
due to higher humidity in the room, the case not being entirely 
tight. 

Fig. 5 shows three curves, all representing resistance standards 
of the Reichsanstalt form. Curve 7 is a i,oocK)hm standard 
(No. 3039) kept totally submerged in oil in a space at nearly con- 
stant humidity of 25 to 30 per cent from January 4 to March 28, the 
resistance decreasing slowly during that period, as the oil dried out 
gradually. From March 28 to April 16 the coil, still submerged in 
the same oil, was in a case at approximately 80 per cent humidity, 
and the resistance rose about 1 7 parts in 100,000. The humidity 
was then reduced to about 25 per cent and the resistance fell off 11 
parts in 100,000 in the same time that it rose 17 parts. This shows 
how great a change can take place in a coil kept submerged in pure 
petroleum oil, when the humidity of the atmosphere changes. Since 
June 25 this coil has been in the atmosphere of the laboratory, not 



Rosa. n 



Babcoek._ 



Variation of Resistances with Humidity, 



131 



[NJO^OOOJNRESirrANCE. 




132 



Bulletin of the Bureau of Standards, 



\Vol.4.No. I. 



in oil, and has increased in resistance about 13 parts in 100,000. 
Curve 9 is a standard io,oooohm coil (No. 1392) kept in air at a 
nearly constant humidity of 25 to 30 per cent from January 4 to 
May 24. Its changes are very slight, showing a small decrease at 
first, corresponding to the coils in oil. Since May 24 this coil has 
been in the atmosphere of the laboratory and has gradually increased 
in value. Curve ^a represents another 10,000-ohm standard (No. 
3040) in air at different humidities, showing, in marked contrast to 
curve 9, large changes due to variation of humidity. Curve 11, 
Fig. 5^J:, represents a 1,000-ohm standard (No. 3057) in air at difiFer- 
ent humidities. The fluctuations in the resistance of the latter 
amount to about 35 parts in 100,000 between the minimum and the 




\i 



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14 24 
1906 



4- 



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I 

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MA'ft 



14 24 



"Ta 



14 24 3 13 23 

1907 



12 22 



Fig. S9i,— Behavior of Wof/f standard coU, 



Curve II is a standard coil, No. 3057, of 1,000 ohms in air, at varying humidities. 



Explanation of airves of Fig. 6, p. ijj. 

The curves of Pig. 6 show the differences in the behavior of resistances of man- 
ganin coils, all of which were wound on wood spools and kept in an atmosphere of 
different humidities, but with different methods of preparation or of mounting. 

Curve 55, 1,000 ohms, wood spool thoroughly shellacked and baked, no shellac on 
outside of wire, no baking of wire. 

Curve 57, 1,000 ohms, same kind of wire wound on similar wood spool, latter 
boiled in |>araffin, no paraffin on wire, no heating of wire. 

Curve 77, 1,000 ohms, on wood spool, wire and spool shellacked and baked and 
then coated with paraffin. 

Curve 25, 1,000 ohms, on wood spool, wire shellacked and baked, and coil then 
.sealed in a test tube by means of a cork and hot paraffin. 

Curve 43, 1,000 ohms, on shellacked wood spool (several coats), wire shellacked 
and baked after winding. Unifilar winding. 



Rosa. 1 
BabcocA,} 



Variation of Resistances with Humidity, 



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(For explanation of curves see opposite page.) 



134 Bulletin of the Bureau of Standards, \vot. 4. J^'o. i. 

maximum of February. As the humidity in the laboratory atmos- 
phere in Washington often goes above 70 per cent in summer (unless 
the air is artificially dried), it will be seen that this coil would be 
very unreliable as a standard. 

Fig. 6 represents five coils of 1,000 ohms each of o.i-mm manga- 
nin wire, wound on wooden spools (mahogany). These curves are 
drawn to a different vertical scale from that used before, one space 
representing a change ten times as great as before. Curve 43 repre- 
sents a coil which was given several coats of shellac and baked in 
the usual manner, the spool as well as the wire being thoroughly 
shellacked. Curve 55 represents a coil in which the spool was thor- 
oughly shellacked, but the wire was not shellacked nor baked after 
winding. Curve 57 represents a coil wound on a similar wood spool 
that had been thoroughly paraffined, but the wire neither paraffined 
nor heated after winding. Curve 77 represents a coil on a shellacked 
wood spool, the wire shellacked and baked as usual and then dipped 
in melted paraffin. Curve 25 represents a coil on a wood spool, 
shellacked and baked after winding, and sealed in a test tube (with 
some calcium chloride inside the tube). The last three coils, in one 
of which no shellac was used and in the other two the shellac was 
protected from the moisture of the air, have remained remarkably 
constant, no change more than i in 100,000 having occurred in 
several months, except in 57, which was due to heating. The first 
two coils, on the contrary, changed as much as 340 and 400 parts, 
respectively, in 100,000. 

Shellacked coils may absorb sufficient moisture in a saturated 
atmosphere to reduce the resistance by leakage, the coils in that case 
showing polarization. A shellacked coil plunged in water absorbs 
moisture very rapidly; in one case tried, the resistance of a coil of 
1,000 ohms decreased about 50 ohms in a short time, showing polar- 
ization strongly. On the other hand, some paraffined coils sub- 
merged in water an hour did not change more than i part in 100,000, 
if at all. These coils were from a box by an English maker and 
had been in use for over four years. This shows that the paraffin 
coating had not become cracked or defective in use. Such coils 
kept submerged in water do indeed absorb moisture and finally 
become polarized, but this is under very extreme conditions. The 
shellacked coils of a Wheatstone bridge, potentiometer, or other 



52^ac*.] Variation of Resistances with Humidity. 135 

resistance apparatus may be dipped in melted paraffin and so be pro- 
tected from moisture. A high grade of paraffin should be used — 
that is, paraffin of high melting point, free from dirt and acid. The 
paraffin coating, of course, slightly increases the lag of temperature 
of the coils when the temperature of the room is changing, but the 
increased error due to this would probably not be a hundredth part 
of the error that may be due to absorption of moisture. 

Since a small and inexpensive coil sealed in a tube or covered by 
paraffin has a very constant resistance, one may possess a number of 
such working standards of resistance with very slight expense or 
trouble, and may have them compared at a standardizing laboratory 
more frequently than bulkier and more expensive standards. We do 
not recommend paraffining resistance standards of precision, but 
rather using such shellacked or varnished coils as have proved con- 
stant when sealed from the atmosphere. We are developing some 
new forms of sealed standards which have proved to be very constant 
during the few months they have been under observation. They 
will be described and the results obtained in measuring them given 
in the near future. 

BFFBCT OF CLIMATE. 

Since the above was in type Drs. Jaeger and Lindeck have 
called attention* to the unfavorable climate of Washington as 
explaining the relatively large seasonable changes observed here in 
shellac-covered resistances. One of us has recently published' the 
results of an examination of the question of differences of climate 
between London, Berlin, and Washington, which seems to explain, 
in a large measure at least, why the changes observed in Washing- 
ton are so mucR greater than those observed in Berlin. 

In order to obtain a fair comparison between the atmospheric 
humidities of the three above-named places, reference was made to 
the official records of the Koniglich Preussischen Meteorologischen 
Institut,* the Royal Observatory, Greenwich,^ and the United States 
Weather Bureau.* From these records the following tables were 



* London Electrician, August 2, 1907. 

* London Electrician, October, 1907. 

*Deutsches Meteorologisches Jahrbuch, fiir 1904 and 1905. 

' Greenwich Magnetical and Meteorological Observations, 1904 and 1905. 

* Report of Chief of Weather Bureau, 1904-5 and 1905-6. 



136 



Bulletin of the Bureau of Standards. \voi. 4, No. t. 



compiled, showing the absolute humidities (vapor pressures in 
millimeters of mercury) and the relative humidities for each of the 
four seasons of the year for the two years 1904 and 1905, for London, 
Berlin, and Washington. The reason for choosing these three 
places was, of course, that observations on standard and precision 
resistances have been carried on for some years past in the national 
laboratories located in these cities. In Berlin no appreciable changes 
in resistance due to humidity have been observed ; in Washington 
serious changes due to this cause have been found, as described 
above ; in London appreciable changes have been reported, but we 
are not as yet aware whether (as seems probably the case) they have 
been found to be chiefly due to the effect of varying atmospheric 
humidity. 

ABSOLUTE HUMIDITY. 

Pressure of Aqueous Vapor in Millimeters of Mercury. 





X904 



5.4 
6.5 
9.9 
7.6 


London 




xgo4 


Berlin 




W 


■ahington 
X905 Mean 




1905 

5.4 
6.3 
10.4 
7.0 

7.3 


Mean 


X9P5 


"•" 


xgo4 


1 . Winter— Dec. , Jan. , Feb. 

2. Spiin«-Mar.,Apr.,May 

3. Summer— Jnn.yjnl., Aug. 

4. Antumn— Sep.,Oct.,NoT. 


5.4 
6.4 
10,15 
7.3 


4.5 
6.2 
9.2 
7.0 


4.5 
6.3 
11.3 

7.1 


4.5 
6.25 
10.25 
7.05 


2.9 

7.0 
14.9 
8.6 


3.0 
7.9 
16.4 
9.1 


2.95 
7.45 
15.65 
8.85 


Mean for tbe year 


7.35 


7.32 


6.7 


7.J 


7.0 


8.35 


9.1 


8.72 



The values for London are the mean of twenty-four hourly obser- 
vations. For Berlin they are the mean of observations at 7 a. m., 
2 p. m., and 9 p. m., which represent the twenty-four-hour average 

RELATIVE HUMIDITY. 





X904 


London 
xg05 


Mean 


1904 


Berlin 


Mean 


W 


■ahington 




xgo4 


1905 

67.5 
68 

79 
77.5 


Mean 


1. Winter— Dec., Jan., Feb. 

2. Spring-Mar., Apr., May 

3. Summer— Jon., Jul., Aug. 

4. Antnmn— 8ep.,Oct.,NoT. 


87 
78 
73 
84 


85 
75 
75 
82 


86 
76.5 
74 
83 


85 
70 
59 
80 


84 
78 
64 
84 


84.5 
74 

61.5 
82 


70 
66 
72 
76.5 


68.75 
67 
75.5 
77 


Mean for the year 


80.5 


79 


79.75 


73.5 


77.5 


75.5 


71.5 


72.75 


72.1 



S2£i»c*.J Variation of Resistances with Humidity. 137 

very closely. For Washington they are the mean of observations 
at 8 a. m. and 8 p. m., which represent the twenty-four-hour average 
approximately, being probably a little too high. 

Table 1 gives the values of the absolute humidities and Table II 
the relative humidities. It will be seen that the figures are very 
nearly the same for the two years. 

The mean vapor pressure for the two years is least in Berlin, 
being a little higher (5 per cent) in London and considerably higher 
(25 per cent) in Washington than in Berlin. The vapor pressure 
is, however, lower in Washington in winter than in London or 
Berlin. 

The mean relative humidity for the two years is lower in Wash- 
ington than in Berlin or London, due, of course, to its higher mean 
temperature. In summer the relative humidity is higher in Wash- 
ington than Berlin, and a very little higher than in London. Dur- 
ing the other three seasons it is appreciably lower than in Berlin or 
London. This is especially noticeable in winter, when both 
absolute and relative humidities are lower in Washington than in 
London or Berlin. 

But as the resistances are kept in the laboratories, whereas the 
above measurements were made out of doors, it is necessary to con- 
sider what difiFerences in the relative humidities existed, on the 
average, between the laboratories and the outside atmosphere. 

In the laboratories of the Bureau of Standards the rooms are 
heated by a mixture of hot and tempered air, forced through a 
double-duct system by large blowers, the temperature of the rooms 
being automatically regulated (usually to about 20° or 21*^ C. in 
winter) by thermostats. In the colder weather the blowers are kept 
going until midnight, and started very early in the morning, so that 
the temperature of the laboratories is kept at about 20® C. most of 
the time and seldom falls below 15*^ at night. The result is that 
the relative humidity of the atmosphere in the laboratories during 
the three winter months probably averages not over 30 per cent 
(allowing for the increase of humidity due to respiration and evap- 
oration within the laboratories). The buildings of the Reichsanstalt 
are probably not heated ta so high a temperature, nor heated for so 
many hours at night, so that the mean temperature for twenty-four 
hours during the three winter months would be considerably lower. 



138 Bulletin of the Bureau of Standards, \voi, 4. No. t. 

whereas the absolute humidity is higher. Hence the relative 
humidity (for twenty-four hours) possibly averages as high as 60 per 
cent during the winter months (allowing as before for some evapora- 
tion within the laboratories). In the summer a laboratory is cooler 
in the daytime and warmer at night than the outside atmosphere, 
having practically the same average temperature as the outside. 
Hence the mean relative humidity would be nearly the same as out 
of doors, or between 60 and 65 per cent in Berlin. In the spring 
and autumn months, due to heating the buildings part of the time, 
the indoor humidity would be somewhat less than outside. Hence 
it would seem probable (always considering the average for twenty- 
four hours) that the mean relative humidity in the laboratories of 
the Reichsanstalt varies comparatively little from season to season. 

In Washington, on the other hand, the average humidity in sum- 
mer (even with some artificial drying during part of each day) is 
more than double that in winter. Thus the differences of climate 
and differences in the methods of heating the laboratory buildings 
combine to make any effects of varying moisture much greater in 
Washington than in Berlin, the difference in climate being as much 
due to the drier winter of Washington as to the damper summer. 

But Berlin is probably no more a representative city in this 
respect than Washington; resistances are used in all kinds of 
climates. The value of a resistance standard or a precision box or 
potentiometer should, of course, not depend on the climate, nor 
require a climate of relatively uniform humidity to enable it to 
remain constant. If a resistance standard is calibrated in Berlin or 
Washington at 60 per cent humidity for example, its value else- 
where will be more or less according to the humidity, if the resist- 
ance is not independent of the humidity. 

Drs. Jaeger and Lindeck give results of recent measurements, 
which show very slight variations, indeed, in a number of standard 
coils of various denominations up to 10,000 ohms, confirming their 
previous work in this respect. Whether these coils were originally 
selected from a larger number because of their exceptional constancy, 
or whether they were differently prepared from those we have been 
getting in recent years, or whether it is partly accidental that the 
humidity varied during May and June of this year so as to leave the 



S^^ifc] Vciriation of Resistances with Humidity, 139 

coils with almost exactly the same values at the end of June that 
they had at the end of April, we do not know. 

The i-ohm standard coils (of the Reichsanstalt form) of the 
Bureau of Standards have fluctuated very little in comparison with 
the changes in the coils of higher values, but they do vary among 
themselves under natural conditions by an appreciable amount, due 
to variations in atmospheric humidity, and these variations have 
been a source of serious concern to us. 

The sealed standards which we have recently devised and have 
been studying for several months differ mainly from those now 
generally used (and known as the Reichsanstalt form) in being of 
smaller size, having closed cases which are hermetically sealed, and 
in having the cases permanently filled with pure oil. The resistances 
are thus oil immersed, and the temperature can be accurately 
obtained, and yet no change due to var>'ing humidity can occur, as 
the thoroughly dried resistances and oil are perfectly protected from 
the atmosphere. 

Our work tends to confirm the work of Drs. Jaeger and Lindeck, 
as the>' very properly observe, not only that manganin is very 
well adapted for resistance standards, but that the method of mount- 
ing the resistances and protecting them from the oxidation of the 
air or oil by shellac or varnish is very satisfactory, provided they 
are also protected from the effects of atmospheric humidity. This 
effect is certainly too great in the higher resistances in general to 
be safely ignored in precision work, whether in standards or in 
resistance boxes. If by some modification in the construction of 
the standards, as Drs. Jaeger and Lindeck suggest, or by sealing 
them from the atmosphere as we have done, the danger of change 
due to humidity is obviated, then they would seem to be all that 
could be expected of wire standards. With resistance boxes that 
are not to be submerged in oil, we have found a coating of paraffin 
over the shellac or varnish to be of value. The temperature coeffi- 
cient of manganin is so small that a slight uncertainty of tempera- 
ture in many cases is not material. With boxes that are to be oil 
immersed the coils (or at least the higher valued coils) may be 
separately sealed in metal tubes, or better the entire box, if properly 
designed, may be sealed. 



i40 Bulleitn of the Bureau of Standards. [ voi. 4. No. i. 

It has been a mystery to us at the Bureau of Standards why the 
manganin standards of the Reichsanstalt remained so much more 
constant than those in Washington. We think the facts given 
above as to the probable difiFerences in the variation of the relative 
humidity in the laboratories of the Reichsanstalt and the Bureau of 
Standards go far toward explaining the difference in the behavior of 
the resistances. It is also possible that, although we have supposed 
the resistance coils to be made exactly alike, it is partly due to some 
difference in their preparation. 

Washington, October 4, 1907. 



THE SELFJNDUCTANCE OF A TOROIDAL COIL OF 
RECTANGULAR SECTION. 



By Edward B. Rosa. 



One of the most carefully constructed standards of self-inductance 
ever made is that described some years ago by Prof. Frohlich, of 
Budapest^ It consists of a large marble ring of rectangular section, 
very accurately ground and measured, and wound with a single 
layer of fine silk-covered wire. Each turn of the wire lies in a plane 
passing through the axis of the ring, the wires being wound as 
closely as possible on the inner surface of the ring and uniformly 
spaced on the outer surface. Taking account of the magnetic field 
within the space occupied by the wire as well as the space within 
the marble core. Prof. Frohlich obtained the following expression 
for the self-inductance of the coil : 

Z= 2n*h [log ri_o.2872l p (^+^+1 log ^l)] (I) 

in which r^ and r„ Fig. i, are the inner and outer radii of the ring 



Fig. I. 
respectively, measuring to the axis of the wire in each case, p is the 



8919—07 10 



^ Wied. Ann., 08, p. 142; 1897. 



141 



142 Bulletin of the Bureau of Standards. {yoi.4sNo.i. 

radius of the bare wire, h is the height o£ the section (center to 
center of wire), and n is the whole number of turns of wire on the 
coil. 

These quantities as determined by Frohlich's were as follows: 

''«= 35-05377 cm 
ri = 24.97478 cm 
h = 20.08455 cm 
p — 0.011147 cm 
« =2,738 

The value found by substituting these quantities in equation (i) 
was 

Z=(o.io2o8928— .oooo9865)io' cm 
=0.10199063 henry s. 

It was assumed in deriving formula (i) above that for a winding 
of fine wire one could consider the current as distributed in a thick 
current sheet, the thickness of the latter being 2p. That is, it was 
tacitly assumed that the flux of magnetic force, and therefore the 
self-inductance, were substantially the same as though the winding 
consisted of n turns of wire of rectangular section, the insulation 
being of infinitesimal thickness and the winding, therefore, com- 
pletely enveloping the marble core. The wire in such a case would 
have a radial thickness of 2p and a breadth on the inner surface of 

the ring of -^, on the outer surface of -^, and on the upper and 
n n 

lower surfaces the breadth would increase gradually from the former 
to the latter value. Such a winding is of course impracticable, but 
was assumed as equivalent to the actual winding of round, insu- 
lated wire. I have elsewhere* pointed out that one can not assume 
a winding of round wires, no matter how fine, to be equivalent to a 
current sheet; and I wish now to show how serious is the error in 
the above case of a circular solenoid arising from this assumption. 
The expression for the self-inductance of the circular solenoid of 
rectangular section enveloped by a thin current sheet is 



■This Bulletin, 2, p. 161; 1906. 



Rosa,^ Self-Inductance of a Toroidal Coil, 143 



r. 



I^:=27l^h\0%-^ (2) 

The correction term ^L as obtained by Frohlich was negative^ and 
proportional to p^ the radius of the wire. For extremely fine wire 
^L would therefore become vanishingly small. 

A thin current sheet would be realized by a winding of infinitely 
thin tape, covering the cor^ completely. The problem is to find the 
diflPerence JL in the self-inductance of such a winding and the 
actual winding of round insulated wire. I have done that* for a 
straight solenoid and the results obtained are approximately correct 
in this case. It may be worth .while, however, to derive the correc- 
tion formulae anew for this particular case. 

The self-inductance of a square of round wire is 

where / is the length of wire in the square ( = 4a) and R is the geo- 
metrical mean distance of the section of the wire. For wires of which 
the diameter is small in comparison with the side of the square this 
is very approximately 

A.= 2/[log£-l] 
For a narrow tape bent into a square the expression for L is 

Z.,= a/[log-l^-i] 

where Rt is the geometric mean distance of the section of the tape. 
The difiPerence is 



i:,-A,=2/riog,^j 



For a wire of circular section ^^^ = 0.3894^/, d being the diameter. 
For a tape of infinitesimal thickness and width Z>, ^^ = 0.22313 Z>. 

Thus^= 1.745^ and 



L,- L„ = 2/ log/i.745^j 



144 Bulletin of the Bureau of Standards. \voi. 4. no. r. 

This is the excess of the self-inductance of one turn of thin tape 
over the self-inductance of one turn of round wire. For the entire 
winding of n turns we should therefore have 



JI^ = 2nl. logi i.745^j 



This is equivalent to the expression previously found* for the case 
of a winding on a circular cylinder, ^irna being twice the whole 
length of the wire as 2;*/ is here. The same result would of coiuse 
follow for a rectangular section not a square. 

In addition to the correction for the difference in the self-induc- 
tances of the single turns is the correction for the differences in the 
mutual inductances upon each turn of all the others. 

The mutual inductances of two parallel squares' is 

where a is the side of either square and d is the perpendicular dis- 
tance between them. If each square is made up of round wire, d 
is the distance between the centers or axes of the wires. If, how- 
ever, the squares are each made up of flat strip, d is the geometric 
mean distance of the two parallel strips, which may be written kd^ 
where k is always a little less than unity,* but nearer to unity as 
the distance d is greater. Putting M^ for the mutual inductance of 
the two rectangles (or squares) of round wire and Mt for that of the 
rectangles (or squares) of thin tape, which will be the same expres- 
sion with d replaced by kd^ it can easily be shown that, neglecting 
small quantities of the second order, 

JM= Aft — J/„. = ^a log, j^ = 2/8, 

which is equivalent to the expression (23) previously found* for 
parallel circles, /^ira being twice the length of the wire, as is 8a 



•This BuUetin, 2, p. 161; 1906. 
'Webster. Elect, and Mag., p. 456. 
*This Bulletin, 2, p. 175; 1906. 



ifosa.] Self-inductance of a Toroidal Coil. 145 

here. As before, it is necessary to compute the value of this correc- 
tion term ^M for all pairs of wires for which it is appreciable. It 
is greatest for two adjacent wires, and rapidly becomes inappreciable 
as the distance increases, so that the fact that the several turns are 
not quite parallel can not make any appreciable difference. It is 
only the small differences in the mutual inductances we have to con- 
sider, and these would not be changed appreciably by inclining two 
rectangles at a small angle. 

For two adjacent wires we have 

SJ/, = 8fllog-j =2/8i 

For two wires separated by one turn 

I 



SJ/g = 8tf log X = 2/2ij 
^2 



and so for each succeeding pair. In an endless ring every wire is 
affected by the same corrections as every other, so that the summa- 
tion will be 

^M^2n\hM, + hM^-^hM^-^ ] 

The values of the hs are given in the first column of Table IV.' 
2S is about 0.332 for 24 terms, being a little greater than in the 
case of a straight solenoid of 25 turns of wire. We may neglect 
the effect beyond 25 turns, and use Table VII for the values of the 
constant A and take B as equal to +0.332 in the expression 

^Z.= -(^A + ^J/)^-2///(^ + i9) 

corresponding to (27) in the previous article. This expression for 
^L is always to be added; when {A-\-B) is negative ^L will be 
positive and will therefore tend to increase the self-inductance. 

In the case of Frohlich's circular solenoid the diameter of the bare 
wire is 



*This BuUetin, 2, p. 178; 1906. 



146 Bulletin of the Bureau of Standards, [i^oi. 4, No. i. 

flf= 0.0223. 
The mean distance between centers of successive turns is 



Z>=29r/^^')= 0.0689 



d 
.-. ^=0.324 



From Table VII, A = —0.57 

-g=+o-33 

^+^=—0.24 

2«/= 2 X 2738 X 60.327 = 330300 cm 

^Z= +79300 cm 

= +0.0000793 henry 
Z.o= 0.1020893 '' 

Z=A+^Z:= 0.1021686 " 

instead of 0.1019906 as found by Frohlich. 
The value of A is positive when the insulation is thin, that is 
when d is nearly equal to Z>. When 



1-745-^= X 



*-> 



the correction term A is zero. That is, for ^^=0.57 approximately. 

For -^ less than 0.57, -/I is negative, and the corresponding correction 

tends to increase Z^. The term B^ being positive, always tends to 
decrease Z^. Hence when A is negative and greater than 0.33 the 
combined correction increases Z^, as in the present case. 

The meaning of this is that the self-inductance of a circle or rec- 
tangle of wire is less than that of a flat strip of width equal to the 
diameter of the wire. As the diameter of the wire is reduced, how- 
ever, its self-inductance increases, and becomes greater than that of 
the strip. So if the solenoid is wound with round wire of very thin 
insulation its self-inductance is less than Z^, the current sheet value; 
but if the wire is finer and covered with thick insulation (its outer 
diameter remaining the same), the total self-inductance increases and 
may be more than Z^. 



ieoM.] Self-Inductance of a Torodial Coil, 147 

To further show the marked effect of spacing the wire, suppose 
the above solenoid has been wound with a double winding of 1,369 
turns each, so that either could be employed, or both, in series or in 
parallel. If both were in parallel and half the current flowing in 
each, the self-inductance would be one-fourth of that just calculated, 
or Z=o.o255223+.ooooi98=.o25542i. 

By Frohlich's formula it would make no difference whether one 
winding or both in parallel were employed as to the value of L. 
But if one winding only is used D is twice as great as before, and 

therefore ^=0.162. 

By Table VII, -4 = — 1.42 approx. 

^=+0.33 



^+^= — 1.09 

— 2«/ {A-\-B)r=z 180,013. 

JL =+0.0001801 henry 
A= 0.0255223 " 



L = 0.0257024 " 

This is greater than the preceding value by nearly two-thirds of i 
per cent. The meaning of this is that when only one winding is 
used there are a great many lines of force immediately surrounding 
the wires, which, carrying the whole current and having more space 
between the wires, give a larger correction term than when the cur- 
rent is divided between the two wires. 

If the wires were very fine indeed (the whole number of wires 
remaining constant), the correction JL would be very great, easily 
several per cent of the value of Z^, whereas by Frohlich's formula 
the correction JL would be approaching zero and the self-induct- 
ance would be simply Z,. 

I have given these examples rather fully to emphasize the serious 
error that may result from assuming a winding of fine wires to be 
equivalent to a current sheet, and to show that for a given spacing 
of the wires the finer they are {beyond a certain point) the greater 
is the error arising from this assumption. 



148 Bulletin of the Bureau of Standards, \voi.4,No.t. 

The straight solenoid oifers many advantages over the circular 
solenoid as a standard. It is easier to construct and measure the 
core and immensely easier to wind, and the calculation of L from 
the dimensions is just as easy and just as certain. 

Washington, August 10, 1907. 



ON THE SELFJNDUCTANCE OF CIRCLES. 



By E*dward B. Rosa and Louis Cohen. 



Various formulae have been given by different authors for the 
self-inductance of circles; that is, for closed rings of circular cross 
section. Some of these formulae are at once convenient and accu- 
rate, while others are both inconvenient and unreliable, and should 
be avoided in numerical calculations. We therefore propose in 
this paper to critically examine and test these various formulae, 
and to show which of them are trustworthy and which are wrong. 
This seems the more necessary inasmuch as some of the latter 
have been g^iven by writers of reputation and they have been 
quoted and used in the belief that they were correct. 

The formula for the self-inductance of a circle was first given by 
Kirchhoff * in the following form: 



L=2/\ log 1.508 

I P 



(I) 



where / is the circumference of the circular conductor and p is the 
radius of its cross section. This is equivalent to the following: 



-j log -^- 1.75 j (2) 



a being the radius of the circle. These formulae are approximate, 
being more nearly correct as the ratio pja is smaller. 

A more accurate expression can be obtained from Maxwell's prin- 
ciple of the geometrical mean distance. The mutual inductance of 
two equal parallel circles near each other is, to a close approximation, 

*Pogg. Annalen, 121, p. 551; 1864. 

149 



150 Bulletin of the Bureau of Standards. \voi.4.No.i. 

where a is the common radius of the circles and b their distance apart 
The self-inductance of a single circular ring is equal to the mutual 
inductance of two equal and parallel circles whose distance apart is 
equal to the geometrical mean distance R of the cross section of the 
ring. Hence 

Substituting in this equation the value of the geometrical mean dis- 
tance for a circular area, R =/»€ = .7788/), we obtain 



i:=47rJ/i +0.1137 |ijlog ^-.0095 |i- 1.75 



(5) 



This is a very accurate formula for circles in which the radius of 
section p is very small in comparison with the radius a of the circle. 
The geometrical mean distance R has, however, been computed on 
the supposition of a linear conductor, and can only be applied to 
circles of relatively small value of pa. We must therefore expect 
an appreciable error in formula (5) when the ratio p^a is not very 
small. Formulae i, 2, and 5 have been deduced on the supposition 
of a uniform distribution of the current over the cross section of the 
ring. 

If the ring is a hollow circular thin tube, or if the current in the 
ring is alternating and of extremely high frequency, so that it can 
be regarded as flowing on the surface of the ring, the geometrical 
mean distance for the section would be the radius p, and we should 
derive from (4) by substituting R=^p^ 



'^Hl"^^^")^^^ 



8^ ^ 



(6) 



In the case of solid rings carrying alternating currents of moder- 
ate frequency the value of L would be somewhere between the 
values given by (5) and (6). 



Rosa. 1 
CotUn.1 



Self-inductance of Circles. 



151 




WIBN'S FORMULA. 

Max Wien * has given what is probably the most accurate formula 
yet derived for the self-inductance of a 
circle. 

If we consider the ring of radius a 
and radius of section ^, Fig. i, to be 
made up of an indefinite number of 
elementary circular filaments, the self- 
inductance of the ring is equal to the 
mean value of the sum of the mutual 
inductances on each filament of all the 
others. If, therefore, we express the 
mutual inductance of an element at P 

on a second element at Q and integrate 

this over the entire area of the section, 
we obtain the mutual inductance of the single filament P on the 
entire ring. Integrating again over the ring we obtain the self- 
inductance of the ring. Wien's result is as follows: 



Fig. I. 



:=4-j(.+ |^)lc«^-.c»83^:-..75, 



(7) 



It will be noticed that the formula differs very slightly from the 
preceding (5). Neglecting the terms in f?^a^ we get from either (5) 
or (7) Kirchhoff's approximate formula. 

If the current be not distributed uniformly over the section of the 
wire, but the current density at any point is proportional to the 
distance from the axis of the ring, Wien's formula for the self- 
inductance is 

3 



.=^(i+| ^1) log ??-.092^--i.75) 



(8) 



which differs very slightly from (7). 

This would apply to the case of a ring revolving about a diametei 
in a uniform magnetic field. 

As would be expected, (8) gives a greater value than (7). 

Rayleigh and Niven gave ' the following formula for a circular 
coil of n turns and of circular section : * 

'Wied. Annalen, 53, p. 928; 1894. 
*Rayleigh*s CoUected Papers, II, p. 15. 

^Neglecting the correction for effect of insulation and shape of section of the 
separate wires. 



152 Bulletin of the Bureau of Standards, \vol /. No. j. 

Z=4--<.|(.+^)l<«^+^.-..75} (.0) 

When «=i, this will be the self-inductance of a single circular 
ring. It agrees with Wien's, except as to one term, which is 

4-- — i instead of —0.008-1 ,. 
24^* *^ a* 

If used for a coil of more than one turn, the expression for L 
(whether obtained from (10) or from one of the preceding more 
accurate expressions) must be corrected for the space occupied by 
the insulation between the wires and for the shape of the section/ 

TESTS OF THE FOREGOING FORMULA FOR CIRCLES. 

For a circle of radius ^ = 25 cm and ^=0.05 cm we obtain from 
the foregoing formulae the following values of L: 

By Wien's formula (7) A =654.40537 x cm 

By MaxweU's formula (5) ^=654.40533 x cm 

By Rayleigh and Niven^s (10) Z, =654.40548 x cm 

By Kirchhoff*s formula (2) Z =654.40496 x cm 

By Wien's sec6nd formula (8) A =654.40617 x cm 

Thus, for so small a value of /> ^ as 3^ any of these formulae is 
sufficiently accurate, the greatest difference being less than i in a 
million, except in the case of formula (8). 

Take for further tests a circle for which a = 25, />=o.5 cm, pa 
being 5*5, and another with ^z= 10, />= i.o, pa being ^'o 

By Wieu's formula 

By Maxwell's formula 

By Rayleigh and Niven's formula 

By Kirchhoff's formula 

By Wien's second formula 

It will be seen that for the smallest ring of radius 10 cm and 
diameter of section 2 cm Maxwell's formula gives a result i part in 
5,000 too small and Rayleigh and Niven's a value as much too large, 
while the simple approximate formula of Kirchhoff is in error by 
I in 500. For the larger ring the differences are much smaller. 

Wien's second formula gives appreciably larger values, as it 
should do. 



P/«=5V 


Pla=^ 


/. =424. 1761 X 


105.497 X 


i:=424.i734T 


105.476 X 


Z. =424. 1 78 1 X 


105.517 «■ 


Z,=424.i464«- 


105.281 X 


A =424. 2326 ir 


105.902 X 



*See Rosa, this Bulletin, 3, p. 1; 1907. 



Rosa. 1 
Coken.A 



Self-inductance of Circles. 



153 



RUSSELL'S FORMULAE. 



In his recent paper in the Philosophical Magazine, Russell * derives 
the approximate expression (2) for the self-inductance of a circle by 
an original method. Assuming that the flux of magnetic force 
through the aperture of a ring is the same as though the current in 



/ 



\ 

\"' 



\\ 







.III 
• ill 



// / 



. I// / / / / 

^-i^T'f-l'-iorf 

-'>-/7 / 



H-»i 



/ 






I I 






o 



\ \ 



\ \ 



\\^^ 



Fig. 2. 



the ring were concentrated in the circular axis of the wire, he writes 
down the expression for the mutual inductance between the two co- 
planar circles, whose radii are a and ^z— r, which is the following: 






where the modulus is 



a—r 



This will be approximately that part of the self-inductance of a 
ring due to the flux through the aperture. 

He then derives the second part of the flux, namely, that inside 
the section of the ring, which he gives as 



^.= 2,r I («-f)^_JV 



f 



*Phil. Mag. 18, p. 428; 1907. 



154 



Bulletin of the Bureau of Standards, 



\V'ol.4,yo. I. 



where Z="'^ -[-- log ^ . 

The integral of this expression for ^g is ira approximately (neg- 
lecting the second term in Z). The total flux inside the section of 
the ring is, however, 2ira nearly. The expression ira results from 
the consideration that these 2ira tubes cut only part of the section of 

the conductor. Hence, multiplying by the factor -| the quantity 

ira results, which is half the flux and is the second term of the self- 
inductance. Adding the two terms, Russell obtains his approximate 
expression for Z, which he shows can be put in the form of (2). 
This is an interesting variation in the method of obtaining the 
approximate value of Z, but in itself gives no indication of the 
degree of the approximation, as do Maxwell's and Wien's methods. 

MINCHIN'S FORMULA. 

Prof. Minchin ' has undertaken to derive the self-inductance of a 
ring by finding the magnetic flux through the aperture of the ring 



\ 






4_cu^,4fl-l-4-4-pr-i-i-frif— - 
^^ / / / / I 1 '' \ \ \ \ v^ 

--';/// / ' ' v \ \\ \-- 

' / / / / \ \ \ \;^N 

''/ i\ \ \\-~ 

Fig. 3. 

and adding the lines emanating from one side of the ring. Thus, 
suppose in Fig. 3, N^ lines pass through the aperture FE and N^ 
lines emerge from the upper surface £fB (taken throughout the cir- 
cumference of the ring), then Minchin's statement is that Ni+N^ 

^Calculation of the coefficient of self-induction of a circular current of given 
aperture and cross section. Phil. Mag. 87, p. 300; 1894. 



Rosa. 
Cok^. 



] Selfiinductance of Circles, 1 55 



is the total number of lines of force linked with and emanating from 
the current, and the number divided by z, the strength of the cur- 
rent, is the " coefficient of self-induction." As this neglects entirely 
all the lines of force wholly within the ring^ which also contribute to 
the self inductance^ Minchin's expression for L is necessarily wrong. 
The large value found in the single example given by Minchin is 
mainly due to an error in calculation, as his formula gives too small 
a value for L. His expression (5) for the flux through the aperture 
is substantially correct, but his expression (8) which contains the 
factor c is very small and does not include the considerable number 
of lines wholly within the section of the wire. Hence the sum oif 
the two (9) which he gives as the coefficient of self-induction is 
wrong. Minchin's expression for L slightly rearranged is as follows, 
where c means the same as p above, 

This expression is derived on the assumption that the current is 
inversely proportional to the distance from the axis. When the 
wire is very small this reduces to 

L — ^ira ( log— — 2 j approximately, (12) 

whereas we have seen above that the second term should be 1.75. 
The difference is due, as just stated, to neglecting the lines of force 
within the section of the wire; but changing 2 to 1.75 does not 
make (11) correct. 

Minchin also finds the expression for the self-inductance for a 
superficial current in the circular ring. This is given in his expres- 
sion (10) and is somewhat greater than the other. Of course the 
self-inductance is less for a superficial current than for a distribution 
through the section of the wire (as we have seen above), whether the 
latter is uniform or inversely as the distance from the axis of the 
ring, as assumed by Minchin. 

Prof. Minchin says that Maxwell gives the approximate value of 
Z for a circle the same as (i 2) above, agreeing with his result. This 
is, however, a mistake. Maxwell gives 



.\ v< '< 






f 



156 Bulletin of the Bureau of Standards, \voi. 4. ao. /. 

Z=47r«Mog ^-2 j 

but R is not the same as c above. R is the geometrical mean dis- 
tance of the section of the wire, not the radius of section. As 
already shown, this leads to 1.75 for the absolute term. 

HICKS'S FORMUUB. 

Prof. W. M. Hicks' has discussed this question from a different 
standpoint and has derived expressions for the self-inductance of a 
ring both for the cases of uniform distribution of current, and for 
current density inversely proportional to the distance from the axis. 
He also has misinterpreted Maxwell's approximate expression for 
the self-inductance of a ring, not noticing that r (as he writes it, R 
as Maxwell wrote it) is the geometrical mean distance of the section 
and not the radius of section. 

Hicks derives two formulse, one for uniform current density and 
the other for current density inversely as r, corresponding to (7) and 
(9) above. Hicks derived his formulse by the use of toroidal func- 
tions and obtained the following expression: 

[72 cos*a+ 3 cos'a+ 4 cos*a 



8 cos 



(13) 

where sin a=-, k^= — ; : a and p are as before the radii of the 

a' i+cosa' '^ 

ring and of its section respectively. 

When the current density is inversely as the radial distance from 

the axis, 

_ ( 4 cos 'a /, , 7 ^v , 4 3 9 , A I + 2 cos a) , ^ 

For pja very small, the terms in k^ may be neglected and cos a= i 
approximately, and we have as before for the approximate value of L 



BPhil. Mag. 88, p. 456; 1894. 



^^] Self-inductance of Circles. 157 

Z=47r«(Iog-^-i.75) 

Taking the three circles previously used to test the formulae of 
Kirchhoff, Maxwell, Wien, and Rayleigh and Niven we have — 

Hicks (13) . . Z„ = 654.38987r 423.8o27r io2.79007r 
Hicks (14) . . Z„=654.40487r 424.130^ 105.2388-^- 

It will be seen by comparing the above results by Hicks's formu- 
lae with those previously given, that these values are in every case 
less than given by Wien's two formulae, and in the case of uniform 
current density less than the values given by any of the formulae, 
even less than by Kirchhofps approximate formula. But the cor- 
rection terms must always increase the value of the inductance. 
Hence, it appears that Hicks's formula for uniform density at least, 
and probably also for variable density, is entirely untrustworthy^ 
the correction terms making the error greater rather than less. 
The approximate formula gives a result too small by ^J^j in* the case 
of the third ring, where p\a^^^ while Hicks's elaborate formula 
gives a result too small by over 2.5% for this case. 

It may be asked how we know the formulae of Wien and Max- 
well to be correct. The answer is that Maxwell's for large rings is 
derived directly from the expression for the mutual inductance of 
two parallel circles using the expression for the geometric mean 
distance of the circular section of the wire, which for a straight wire 
is an absolute expression, not an approximation. Hence, because 
they agree we know that for large circles {p\a small) both Maxwell's 
and Wien's expressions are correct to a very high degree, and since 
for the third circle they agree to i in 5000, we may safely assume 
they are quite accurate for that case also. The correction factor is 
positive for large circles and must always be positive. 

Hicks's formulae were derived by a very elaborate process, which 
involved successive approximations. It is evident that the errors 
occurring in these approximations exceeded the total value of the 
small correction terms which it was the object of the investigation 
to determine. 

8919—07 II 



158 Bulletin of the Bureau of Standards, \voi.4,No.t, 

BLiXHY'S FORMULA. 

Bldthy* gave an expression for the self-inductance of a circle 
which he supposed to be exact, and also expanded it into a more 
convenient form for calculation, the latter being presumably accu- 
rate to a very high degree. 

The following are BI4thy's formulae, the first being the so-called 
"exact expression: '' 



T . (i Aa^p+Ji6a*^9tap , 16a* 
Z.=4^.^1og, ^—^ ^+^ 

Z=4^ajo.57944+log.^-^^-^.-^-..} (i6) 

Calculating the self-inductance of the above circles by the first 
of these formulae, we have, 

For largest circle, « = 2 5 p= 0.05 Z. = 676. 2056ir 
For second circle, ^1 = 25 /»=o.5 L= 449.48357r 

For smallest circle, ^5=10 /»=i.o Z— ii5.9656ir 

Comparing these results with the values by the formulae of Max- 
well, Wien, and Kirchhoff we see that the first is in error by 3.5%, 
the second by 6%, and the third by 9%. The second formula gives 
substantially the same results. 

Neglecting the three smallest terms in the second formula it may 
be written 



L=47ranog J ' 1.50J 



The absolute term should be 1.75 instead of 1.50, and this accounts 
for the principal part of the error in the results by Bldthy's formulae. 
Examining his method, we see that two assumptions have been 
made that are not permissible. The first is that one may integrate 
continuously up to the center of the wire in finding the total flux 

* London Electrician, 24, p. 630; April 25, 1890. 



^JJ; ] Self-inductance of Circles. 1 59 

through the ring, and the second in assuming that all the lines 
within the ring cut the entire area of the section of the ring. This 
necessarily gives too large a value for L^ and makes Bldthy's for- 
mula entirely unreliable. 

Bldthy's formula is often given," apparently because it is a 
simple formula and was supposed to be very exact. But Kirch- 
ho£F's is much simpler, and, as the three examples given show, is 
amply accurate for most cases. 

We thus see that Kirchhoff 's simple approximate formula (2) is 
not only very convenient, but for many cases amply accurate; that 
the formulae (5) and (6) derived by means of Maxwell's principle of 
the geometrical mean distance, and formulae (7), (8), and (9), derived 
by direct integration, are very accurate for all cases except where 
the cross section of the ring is very large in comparison with the 
radius a; and that the more complex formulae of Minchin, Hicks, 
and Bldthy are wrong as well as inconvenient, and should be avoided. 

Washington, August 10, 1907. 

"HeydweiUer (Elektrische Messungen) gives only Bldthy's formula for circles. 



THE INFLUENCE OF FREQUENCY ON THE RESISTANCE 
AND INDUCTANCE OF SOLENOIDAL COILS. 



By Louis Cohen. 



The resistance and inductance of a conductor depend on the dis- 
tribution of the current within the conductor. When the current 
is continuous the distribution is uniform throughout the section of 
the conductor, and the problem of finding the resistance and induc- 
tance is a verj' simple one. If, however, the current is varying with 
respect to time, eddy currents with their accompanying magnetic 
fields will be generated within the conductor, which will alter the 
distribution of the current and consequently change the resistance 
and inductance of the conductor. The problem of finding the law of 
variation of resistance and inductance with the frequency is of consid- 
erable importance, and for the case of a straight cylindrical wire the 
problem has been satisfactorily worked out. The results, however, as 
obtained for the case of a straight wire, will not hold when the same 
wire is wound into a coil. It has been found experimentally that 
the change in resistance of a coil for any given frequency is much 
larger than if the winding of the coil were drawn out into a straight 
conductor. Dolezalek,* in his experiments with high-frequency 
currents, was the first to call attention to the fact that the change of 
resistance is larger than that calulated by the theory for straight 
conductors. Battelli and Maggi have also carried out a series of 
experiments along that line and found the same results. 

Owing to the importance of the problem in its application to 
wireless telegraphy, several investigators have sought to obtain 
solutions to this problem. Their efforts were not attended by any 

^Dolezalek, Annalen der Physik, 12; 1903. 

161 



i62 Bulletin of the Bureau of Standards, \voi.4.no.i. 

high degree of success, inasmuch as the results obtained do not 
agree with experimental facts. 

Max Wien," who first investigated the problem, obtained a solu- 
tion in a form which is rather a slow convergent series, and the 
calculation of the various terms is very laborious. Independently 
of this inconvenience, which Wien himself pointed out, his theory 
is not correct, as was shown by Battelli, since he implicitly assumes 
that the distribution of the current in the section of the wire is the 
same at all points at the same distance from the axis. Sommer- 
feld,' who made the next attempt to get a solution to the problem, 
also failed to obtain an agreement between his theoretical conclu- 
sions and experiment. According to Sommerfeld's theory, the 
change of resistance of a coil will be independent of the width of 
the winding — that is, if we replace one turn of lo mm in width by 
ten turns of i mm in width, but of the same thickness, then the 
change in resistance will, in accordance with Sommerfeld's theory, 
be the same. This appears to the author to be incorrect; for 
apriori we can say that the change of resistance must be a func- 
tion of the section of the winding. Recently another solution of 
the problem was given by G. Picciati,* but unfortunately his theo- 
retical results fail also to agree with experimental results. 

The table on page 1 70 shows to what extent the values calculated 
by the various formulas, for the per cent change in resistance, differs 
from the experimental values. From the table it can readily be 
seen that none of the formulas derived by the various investigators 
agree with experimental results. 

The question of change of self-inductance is not of such practical 
importance as the change in resistance, and there are no experi- 
mental results on record by which we could verify any theor)\ 
The problem was discussed by Wien, but the same criticism which 
was offered to his work on the change of resistance will also apply 
to his work on the change of inductance. Doctor Coffin* has 
recently contibuted two papers on the change of inductance of coils 
with frequency. He has not, however, developed any new theorj', 



*M. Wien, Annalen der Physik, 14, p. i; 1904. 
'Somnierfeld, Annalen der Physik, 15, p. 673; 1904. 
*G. Picciati, II Nuovo Cimento (5), 2, p. 351. 
*This Bulletin, 2, p. 275; Physical Review, 22, p. 365. 



G>k€n,] Influence of Frequency on Coils, 163 

reproducing Sommerfeld's work with such modifications as to obtain 
the change in inductance in place of resistance. 

In view of the above considerations, it appeared to the author 
desirable to investigate the problem anew, and it was very gratify- 
ing to find that the results obtained agree with experiment. My 
conclusions are that the change in resistance of a coil is a function 
of the frequency, the section of the winding, and the pitch of the 
winding. 

Suppose we have a very long solenoid, and the windings very 
close together, so that we may assume the magnetic field within the 
solenoid to be uniform all the way through, even close to the wind- 
ing, and parallel to the axis of Z; the field outside the solenoid will 
be zero. Let us suppose the section of the winding to be square, 
and consider now the electric and magnetic distribution in a single 

nnnnnnnnnnnnnnnnnnmnnn 



ZAXI8 



I 



- d d 

uuuuuuuuuuiauuiduuuuuuuu 



Fig. 1. 



winding. The electric force will be circular, centered on the axis 
of Zy while the magnetic force will have two components, one radial 
and the other longitudinal, parallel to the axis of Z. 
Let E denote the electric force. 

Af " the longitudinal component of the magnetic force. 
L " the radial component of the magnetic force. 
/i " the current at any point in conductor due to varia- 
tion of magnetic field within conductor. 
/ " the total current in conductor. 
a " the conductivity. 

d " width or breadth of section of winding. 
The connection between electric and magnetic forces are as follows: 

Curl (magnetic force) = 47rX current. 

Curl (electric force) = rate of variation of magnetic force 
with respect to time. 



dM 
dr 


dL 
"dz'' 


= \ircE 


-dE 


dL 




dz 


' dt 




dE E 
dr r 


dM 
dt 



164 Bulletin of the Bureau of Standards, \voi, 4. a«. /. 

In this particular case these relations can be expressed in the fol- 
lowing form: 



(I) 



From the above three equations we can easily deduce the following 
equation of propagation : 

cPE idE E (PE ^ ,. 

If the impressed force is simple harmonic with respect to the time, 
we can put 

E—u cos mze"^^ 

where u is function of r only, and m is any arbitrary constant. 
Introducing the value of E into equation (2) we get the following: 



d^e 
1? 



+-^S+(-*--P>- (3) 

The solution of equation (3) will be 

u = Af,(ikr)^ B Y^ikr) 

Ti and Fj are the Bessel functions of the first and second kind, and 
of the first order. The complete solution of equation (2) will be 

£'= \aJ^ {ikr) +BY, {ikA cos w^^>' (4) 

The values of L and M may be obtained from equation (4) by the 
aid of the relations between the electric and magnetic forces as 
given by equations (i), thus: 



cMm.] Influence of Frequency on Coils. 165 

L = -^(4/, {ikr) +BY^ {tkr)\ sin me^f' (5) 

^=^+ ^waE = C^ +4ira)U/, (tkr)+BV,{tkr)\ cos jm^^X- 
= fr\A/x {tkr)+BV,{tkr)\ cos /w^iJ-X 

4/, (iifer) + ^ r, (?>fer)| cos mee'^' (6) 



dr 



-7 



/o and }^ are the Bessel functions of the zero order. 
Since m is an arbitrary constant, we can choose the value of m so 
as to suit the conditions of the problem. 
Let us put 

w = ^ (« = i> 3) 5. 7. ) 

a 

and since ^ is a function of w, k will also have an infinite number 
of values. If we now put 



^=-^i'r-'A',B^-^Air'B' 



nir ^ nir 



then the values of E^ Z, and M will be given by the following 
expressions: 

E=i\^A',J,{ik,.r)+B',. Y,{ikA^_^ {t)»-^ cos ^ ^>' 
L=l'l^\^A',J,{ik,.r)+B', y,(tk„r)U^ (0-> sin -"J-^>' [ (7) 

Af=l.^ -^^}^A'J,{tk„r) + B^,, Y,{ik„r) \;^J^y-' cos -^- ^>' 

If the solenoid is of considerable length the magnetic field within 
the solenoid will be constant and equal to the magnetizing force, 
which is 4^57 where I is the total current and S the number of 
turns per unit length, and the field outside the solenoid will be 
zero. 

At the surfaces of the solenoid, M^ the longitudinal component of 
the magnetic force within winding, will be the only one acting; 



i66 



Bulletin of the Bureau of Standards, 



\Vol.4sNo.i. 



and to satisfy the condition of continuity we must have the follow- 
ing relations satisfied : 



l.^\A>Jlik,a)^B\ n (/>fe,a)j£(0-' cos ^>'=4^^/^^>' 
^^\A\UiKb)+B'„ K.(/>fe„*)j^^^(/)'-' cos ~^P'=o 



(8) 



{a is the internal and b the external radius of the solenoid) 

These two equations will be satisfied if we determine every set of 
A^ and B' from the following equations : 



KP{A\UiKa)-^B\, Ylik^a)\^.^irsl\ 
{A\JliKb)\B^,, Ylik,b)\ = o I 
Then the first equation of (8) will reduce to 

47rj/3 jcOSTTZ — - cos^-7- + -cos^-3 — . . 



(9) 



— ^irsl 



(10) 



Now since the series in the brackets for the interv-al — _ to+_ is ^ 

2 2 4> 

equation (10) is an identity, and consequently the conditions as 

expressed by equation (8) will be satisfied. 

The constants A* and B\ as determined by equation (9), are as 

follows: 



A\= 






B'=- 



'-fjliKb) 



(") 



Jlik„a) YlikJ,)-J,{ik^b) Y,{iKa)\ 
If we denote by /, the current at any point in the conductor, then 

4 , .._ . nirz 



I^ = aE—a 2 



A'„J,{ik„r)+B\Y,{iKr) 



— (^)'— ^cos — r ^^ 
nir ' d 



The heating effect produced by the current /, in a given volume 
will be 



///■ 



Cakem.} Influence of Frequency on Coils. 167 

and it must be remembered that this heating effect is produced by 
the eddy currents only. In addition to that there is of course a heat- 
ing effect due to the current flow in the circuit. 

Considering, however, only the eddy currents, we may look upon 
the heating effect as if we had a resistance R and a current / pass- 
ing through it that is 



m 






Considering our volume as that of a single turn, we have 

Jo Ja J^d <^ 

2 

Introducing the value /*„ we get 

y, {ik„a) K. {ife^b ) - /. (iKb) n {tk„a) nir """^ d] ^^^'^f'^^^^V 

Since, however, 



X 



ws irz 



Qosp -J- cos q -j-dz^o 
d d d 

Where p and q are two distinct odd numbers, therefore in calcu- 
lating (12) we must only consider the square of each term and 
neglect the product terms, and therefore 

d 

a 

I y, { iknb)L iik„r) - / . {tk„b) F. {tk„r)\ ,.,„_, , nirz , 

\j.{ik„a)Y,{tk„b)-J,{ik„b)Y-{ik„a)\^'^ ^°* d 



i68 Bulletin of the Bureau of Standards. \voi. 4. no. /. 

= 256 ^f^aird 



; {tk,,a) n (^•>&n*)-/o {t^nb) v. {t'Ka)\ ^ ^ ^ ^^ 



Now, 



^ = w*+ 47rc«^ = (a+ ^^) say 
and, therefore, 

Even if we shall neglect /w* as compared with i67r'<r*/*, then the real 
part of k will be 

where / is the frequency. 

If the winding is of copper, then a-=5.9X io~*, approximately, 
and if we assume /"to be 2,000, 
then. 



a — 2V5.9 X 10 * X 10 X 2 X 10' = 7, approximately. 

If r=5 cm, say, then the real part of kr will be a large quantity, 
and we may therefore substitute for the BessePs functions their 
approximate values, which are as follows:' 

/o {i^^) = -, ^— , /i {ikr) = . : . ^ 

^27rkr V27r^r 



• See Gray and Mathews Treatise on Bessel Functions, p. 156. 



cokem.] Influence of Frequency on Coils. 169 

Introducing these values in equation (13) we obtain the following: 

= 256 s*p^irda<r 






)^(*ii+«Pn)(*-r) _j_^-f«»+«^i.)(*-'')|« 
^-(•„+«^n)rf_^(«n+«PnJrf K^ 

In working, however, with complex quantities the real part of the 
squares of a complex quantity can be obtained by multiplying the 
quantity by its conjugate. In this case the conjugate is obtained 
by substituting — / for i everywhere in the expression, and this will 
give 



/b n=» 



cosh2an (^— r)+cos2/8„(^"-^) ^ 
cosh2a„^— cos2/8„^ 



woo 



COsH2a^^— COS2^n^ 

When d is small (i or 2 mm), and the frequency is fairly high, 
then to a very high degree of approximation we can neglect 
s\n2l3^d and cos2/8„flf as compared with sinh2a„flf and cosh2a„fl^, 
and under these conditions sinh2a„// will be very nearly equal to 
cosh2aA^, and therefore equation (14) will reduce to 

i?' = 1 28 s*/^-rrada Y^ .. .!_^.. (15) 



170 



Bulletin of the Bureau of Standards, \voi, 4, nc /. 



The value of R'y as given by equation (15), represents the increase in 
resistance due to the variation of the electric and magnetic fields 
within the material of conductor. In addition to this we have of 
course the ordinary resistance of the wire which it offers to direct 
current, and if we denote this resistance by R^^ then the total resist- 
ance will be 

R=R' + R,. 

The following table gives the values of (per cent change in resist- 
ance) for two different coils and three distinct frequencies. Column 

R' 
one gives the experimental value of ^ as determined by Wien/ 

R^ 

and the other columns gives the values of ^- as calculated by 

various formulae. R is the direct current resistance of coil, and R' 
is the change in the resistance due to frequency. 

TABLE. 
Coil I. r-0.0485 cm. s=8.75. 



Frequency 



measured 



R' by Wien*s 
R formula 



R'by Sommer ' R'byPlcciati R' by formula 
R feld's form R formula | R (15) 



2rX4050 
2rX5680 
2rX8310 



0.021 
0.045 
0.089 



0.023 
0.045 
0.100 



0.042 
0.080 
0.165 



0.032 
0.062 
0.125 



0.023 
0.044 
0.090 



Cofl II. r=0.1 cm. s=4.57. 



2TX4050 


0.34 


0.521 


0.58 


0.45 


0.365 


2TX5680 


0.60 


1.045 


0.94 


0.75 


0.59 


2rX8310 


0.89 


2.053 


1.37 


1.11 


0.89 



The agreement between the observed values and those calculated 
by my formula is exceedingly good, which shows that the deduction 
of the formula on the assumption that the winding is of square sec- 
tion leads to accurate results. The formula (15) is very convenient 



' Loc. cit. 



cok^.] Influence of Frequency on Coils. 171 

for calculation, the series is very rapidly converging, in fact for all 
ordinary cases where the wire is fairly fine and the frequency is 
anywhere above 2,000, the first term will suflfice. An examination 
of equation (15) will show that the change in resistance is a function 
of the frequency, of the diameter of winding, and also of the number 
of turns per unit length or the pitch of the winding. 

When the frequency is very high, say lo*, and the diameter of the 
wire is not exceedingly small, then the value of ^ as given by 
equation (15) will reduce to a still simpler form, for in that case we 

may neglect —^-^ as compared with 16 tt* <r*/*, and the value of a and 

)8 will be as follows: 



Introducing these values of a and /8 into equation (15) we get 

^, _ 1 28 s'/' wdaG^^s^ I 
A^^P^2nap ;^«" 

The resistance per unit length is / 

The total resistance will be 

=J?.ji+45*V/^rf«2^.} (16) 

It is interesting to compare the resistance of a solenoid at such 
high frequency with that of a straight wire of same length. The 



172 Bulletin of the Bureau of Standards. \vol 4. No, r. 

resistance of a straight cylindrical conductor per unit length at a 
very high frequency is 



R=^\pR. = R..y^ 



= R~^d4^f 17) 

Now, if the frequency is very high, we can neglect unity as compared 
with the remaining term in (16), and therefore the ratio of the 
resistance of coil to that of straight conductor will be 

R 
Equation (18) shows that for high frequencies the ratio — ^ is inde- 

pendent of frequency, the ratio increases as the square of diameter 
of wire and inversely as the square of the pitch. The same conclu- 
sions were arrived at by Battelli by an entirely different method, 
and were verified by Blake experimentally. 

EXPSRIMENTAL RESULTS. 

Though my theory agrees so closely with the experimental results 
of Wien, yet it was thought desirable to verify it further by addi- 
tional experiments. Professor Pupin kindly consented to let me 
use his high-frequency machine, and the experiments were therefore 
conducted in his laboratory. The method adopted in measuring 
the resistance was the ordinary bridge method. To balance for the 
inductance I used a torroidal coil, which Professor Pupin had in his 
laboratory. The coil is wound with stranded wire of very small 
diameter, the whole diameter of the wire not being more than 0.2 cm, 
and this is made up of 30 wires, so that we can safely neglect the 
change in resistance in the balancing coil. As a detecting instru- 
ment I used a tuned telephone which Professor Pupin employs in 
some of his investigations. It is probably 50 times as sensitive as 
the ordinary telephone receiver. The method of procedure was to 



Cok^.] 



Influence of Frequency on Coils, 



^7i 



determine the resistance of the coil by direct current, and then to 
measure its resistance in the bridge for alternating current. Two 
solenoids wound with wires of different diameters were employed. 
The frequencies were maintained constant by the aid of a tuning 
fork. 

The dimensions of the coil are as follows : 
Coil I : 

Internal radius of coil 
diameter of wire 
Number of turns per cm 
total number of turns 
resistance of coil 
Coil II: 

Internal diameter of coil 

diameter of wire 
Number of turns per cm 
total number of turns 
resistance of coil 
The results obtained are given in the following table : 

Coin. 



= 4.961 cm 


= 0.29 cm 


= 3-1433 


= 476 


= 0.441 ohms 


= 4.961 cm 


= 0.206 cm 


= 4.319 


= 580 


= 1.028 ohms 



Frequency 


-^ measured 

0.0159 
0.091 


^ calculated 


2TX1280 
2tX896 


0.160 
0.084 


Coil II. 


2irX1280 
2irX896 


0.052 
0.027 


0.044 
0.022 



The experimental values of the resistances could not be relied upon 
within .005 ohms, and hence the values may be modified slightly, 
which may either improve the agreement between the calculated 
and measured values or make it worse. The small difference 
between the measured and calculated values may be accounted for 
8919 — 07 12 



174 Bulletin of the Bureau of Standards, \voi. 4. No. t. 

if we bear in mind that, to get the final expression for the change in 
resistance, we have replaced the Bessel functions by exponential 
functions which is more nearly true as the argument gets large. 
Now, since the argument is a function of the frequency and of the 
radius of coil it is evident that for higher frequencies the approxi- 
mation will be closer than for lower frequencies and this may 
account for the small discrepancy at the lower frequency. By final 
formula (15) therefore as it stands will hold absolutely for all cases 
where the argument {kr) is fairly large, say, 20 or more, which 
implies a fairly high frequency, perhaps 1,500 or more, and the 
radius of the coil must not be very small. We can of course vary 
the two factors, making one very large and one very small, but so 
long as the product kr is not small the formula will hold. If we 
have a low frequency and the radius of the coil is also small, then 
the final expression (15) will not be strictly true, and it will approx- 
imate the true value as kr gets larger. 

CHANGS IN INDUCTANCE. 

The change of inductance can be obtained by a method similar 
to that employed in obtaining the change in resistance. In this 
case we make use of the equality of electro-magnetic energy and 
electro-kinetic energ>'. 



4j/,v.=i^/. 



/=^^^J^rf. (19) 

Now 

The values of L and M are given by equations (7) 



Co/k^M.] 



Influence of Frequency on Coils, 



175 



Introducing the values of the constants A' and B' from equations 
(11) and using the approximate values of the BeSvSePs functions we 
get: 















-_ cos-— ^ 

^r ^ 



Now 



ir=v-^Ar 



and since //i Z,, and M are complex quantities, the square of the 
amplitude can be obtained by multiplying the quantity by its con- 
jugate, which in this case will be merely putting (-/) everywhere 
in place of (/), and this will give us 



//»_\n 2 56 j'/' 






+ 



YI256 jV'|^«<*-'^^— ^-''^«^*-'^)— ^-2'^»^*-'^)— ^'^"(*-'^ 



Zj /^* 



^*fi rf— ^ -2anrf_ ^ -2l^«rf__ ^2/^„rf 



cos' — , 



naoo 

S256 J*/' Jcosh 2a„(*— r)— COS 2 fin{p — r] 
«"(a,.*+/3„*( cosh 2a„^— COS 2 A.<^ 



« . nirz 
-sin--, 
r d 



(21) 



yi256^ //'j cosh 2an(^— /^)— cos 2fiJ^b'-r ^ 
L^ n* \ cosh 2a„^— cos 2/9,,^ 



For one single turn, 



- COS — r 
r d 



fPrdrdzde^2Tt 



II: 



IPrdrdz 



1 76 Bulletin of the Bureau of Standards. Wol 4, No, i. 

and 



"---'It: 



£> = ~p I ^^^=Ai I I ^IPrdrdz 



2 

Introducing value of //* from equation (21) we get: 



/=I28/J y^ I 1**1 I cosh2o„(^- r) - cos20„{d~r) 
L^Ja J-1 W+^n' cosh2a;,rf-cos2y8„rf 

2 



a' 



nirs 



sm rf 



' cosh2a„^— cos2/8„flf <gf ) ""J 

= 128 s^aJy^lj[^'+i%^^^ (22) 

When the frequency is very high and the diameter of wire is not very 
large, a will be a large quantity and equation (22) will reduce to 
the following: 

This is the inductance due to the magnetic field within the mate- 
rial of winding of a single turn, and the inductance due to the total 
number of turns will be 

Where / is the length of the solenoid. The change in inductance 
will be the difference between the inductance, due to magnetic field 
within the material of the coil, when the current is continuous and 
alternating. For continuous current the inductance due to mag- 
netic field in the material of the winding alone is' 



"^Heaviside collected papers, i, p. 356. 



coJk€n.] Influence of Frequency on Coils, 177 

Hence the change in inductance £! will be 



L^^fdl 



ntBoo 



(26) 



The per cent change in inductance will be the ratio of change in 
inductance to the total inductance of solenoid. Now the total 
inductance of solenoid consists of two parts; one due to magnetic 
field within the solenoid, and the other due to magnetic field within 
material of the windings, thus: 

o 
If a is not very small, then we may put 

/ = 47rV/^«. 
If we denote the per cent change in inductance by /g, then we have 

/ — ^ . 

^* 4,rV/» 



Mm OP 



ina 



As an example, suppose ^ = 5 c\\\*d—o,2 cm, ^ = 4 
and 

^ = 27rX lO* a' = /S* — 23.6X 10', a=i54 
and 

^Xio-i6x4j^{i + J+ • • •) 

^^ ^^^^ ^— —0.025 approximately. 



0.2 



The change in inductance for this particular case is about 2.5 per 
cent 



178 Bulletin of the Bureau of Standards, \voi. 4, nq. r. 

Rksume. — To sum up the results of this investigation we can say 
that the theory developed in this paper for the change in resistance 
and inductance of solenoids due to frequency is fully corroborated 
by experimental facts. The final expressions given by equations 
(15) and (26) are very simple and convenient for calculation, and 
will give accurate results in all cases except when the frequency is 
exceedingly low. For convenience of reference I reproduce here 
equations (15) and (26), indicating also the meaning of the factois 
involved. 

HsOO 

R' is the change in resistance due to frequency. 

£f u u a a inductaUCC " " 



m 



'+V^*+i67rV/' 



2 



w-^ (''=i> 3. 5> 7, 9 ) 

d denotes diameter of wire. 

a " conductivity. 

p ^' 2ir frequency. 

s ** number of turns per unit length. 

a *' internal radius of solenoid. 

/ " length of solenoid. 
In conclusion, I wish to express my thanks to Prof. M. I. Pupin, 
of the Columbia University, for his kindness in permitting me to 
use his private laboratory, where the experimental part of the work 
was carried out, and I also wish to thank his assistant, Mr. W. E. 
Cushman, for his kind assistance in the experimental work. 
Washington, August 16, 1907. 

O 



THE ATOMIC WEIGHT OF HYDROGEN. 



By William A. Noyes. 



Some years ago the writer* carried out a series of determinations 
of the quantitative composition of water, from which the value 
15.896 was calculated for the atomic weight of oxygen on the 
hydrogen basis. The opinion was expressed, in the paper, that the 
true value was probably within one part in a thousand of this num- 
ber and that it was rather below than above the value reported. 
Several years later Morley* published an account of his elaborate 
determinations of the densities of hydrogen and oxygen and of the 
composition of water by weight, which led him to the value 15.879 
for oxygen, or i .00762 for hydrogen (O = 1 6). Meanwhile Richards ' 
had shown that copper oxide retains occluded gases obstinately, a 
fact which was partly known to me at the time of my work, but 
which was not as carefully considered as it should have been. There 
was obtained in each of my experiments, at the end, a small amount 
of gas which was assumed to be nitrogen on the basis of one or two 
rather imperfect analyses of the earlier samples. The weight of 
this gas, calculated as nitrogen, was subtracted from the weight of 
the hydrogen, giving, on the average, a correction of about one part 
in a thousand. Several years after the publication of Morley's 
results it occurred to me that this gas came, very probably, from the 
copper oxide, and that its weight should be subtracted from the 
weight of the oxygen instead of from that of the hydrogen. On 
applying the correction in this manner the value 15.879 (or 1.00765) 
was found. 

'Am. Chem. J., 12, p. 441; 1890. 

'Smithsonian Contributions to Knowledge, 1895. Am. Chem. }., 17, p. 267 and 
p. 396; 1895. Z. phys. Chem., 17, p. 87; 1895. 
'Ftoc. Am. Acad., 26, p. 276; 1891. 

179 



i8o Bulletin of the Bureau of Standards. \yoi. 4, m. 1. 

While this agreement with Morley's value was giatifyitig, and 
the fact was stated to a few personal friends, it did not seem proper 
to publish a statement about the matter until the surmise could be 
confirmed by new experimental evidence. 

In addition to the desire of confirming or refuting the above 
explanation of my earlier results, several reasons have made it seem 
worth while to undertake a new determination of this constant. 
Hitherto our accurate knowledge of the composition of water has 
rested on Morley's work alone. He secured so high a d^ree of 
concordance in his results, and he exercised such an extraordinary 
degree of care at every point that the results obtained by all other 
observers must be considered as having only confirmatory value, in 
comparison.* It seemed worth while, if possible, to secure a similar 
order of accuracy by a difEerent method. 

Richards and Wells* have recently given us a very accurate 
determination of the ratio between silver and chlorine, but the exact 
value for the atomic weight of chlorine is still in doubt, because 
the ratio between silver and oxygen is not satisfactorily known.* 
A determination of the ratio between hydrogen and chlorine has 
been carried out at this Bureau, and by using hydrogen generated 
in the same manner for that determination and for the determina- 
tion of the composition of water a very direct comparison between 
oxygen and chlorine has been secured. As the atomic weights of 
more than forty elements have been determined in their relation to 
silver or the halogens, or both, the fundamental importance of the 
ratios of chlorine and silver to oxygen is apparent 

Finally, it seemed possible so to carry out the work as to secure 
some evidence with regard to the question of change of weight in a 
chemical reaction in which a large amount of energy is dissipated. 
This phase of the problem was suggested to me while considering 
the claim made by Professor S. M. Babcock some years ago that 
ice loses weight when it melts. He proposed the theory that the 
loss of weight was intimately connected with the gain of energy by 
the ice as it melts. If this were true, hydrogen and oxygen should 
gain weight when they combine to form water. It may be said, at 

♦This will be discussed further in a later paper. 

*J. Am. Chem. Soc., 27, p. 459; 1905 • 

*Guye andTer Gazarian, Compt. Rendus, 143, p. 411; 1906. 



iM^ef.] The Atomic Weight of Hydrogen, i8l 

once, that the results to be given are not conclusive on this point. 
So far as they have any bearing on the question they indicate a loss 
rather than a gain in weight when hydrogen is converted into water. 

Apparatus. — ^The apparatus used in the work was, in part, very 
similar to that used in the previous investigation.^ Five series of 
determinations have been carried out In the first four of these the 
hydrogen and oxygen were obtained by the electrolysis of dilute (15 
per cent) sulphuric acid. In the last series the gases were generated 
by the electrolysis of a 6 to 8 per cent solution of barium hydroxide. 

The purifying train will be easily understood from the figure. 
In the first three series of experiments, and in all but the last three 
determinations of the fourth series, the hydrogen was passed at first 
through a tube of common glass filled partly with platinized asbestos 
and partly with copper gauze, and the oxygen was passed through 
a similar tube filled partly with platinized asbestos, partly with 
asbestos mixed with lead chromate. These tubes were heated to 
300^-350? In the last three experiments of the fourth series hard 
glass tubes were substituted for the common glass, so that a higher 
temperature could be used, and in the fifth series hard glass tubes 
filled with platinized quartz were used. The platinized quartz was 
prepared by moistening the quartz, which had been heated and 
quenched in water, with a solution of chlorplatinic acid, and reduc- 
ing the latter in a current of hydrogen. Each gas then passed 
through a serpentine tube about 4 meters in length and of 8 mm 
internal diameter. These tubes contain a 15 per cent solution of 
potassium hydroxide in which was dissolved a small amount of lead 
oxide. Sulphur compounds present in the hydrogen were reduced 
to hydrogen sulphide as the mixture passed over the platinized 
asbestos and copper, and the sulphur of the hydrogen sulphide was 
retained by the lead as lead sulphide. Only a very small amount 
of lead sulphide was deposited during the passage of more than 
1,000 liters of hydrogen through the asbestos. When the barium 
hydroxide was used as an electrolyte, the serpentine tubes were 
replaced by btdbs to collect the condensed water and the solution 
formed by the deliquescence of the potassium hydroxide. The 
union between the hard and soft glass was made by grinding the 

^Am. Chem. }., 12, p. 441; 1890. 



l82 



Bulletin of the Bureau of Standards, ivoi. 4. no, 2. 

1+ 





Noyes.] The Atomtc Weight of Hydrogen. 183 

joint and then melting in it a very small amount of Khotinsky 
cement. Ample evidence is given below that these joints were 
perfect. 

The gases passed next through the tubes containing potassium 
hydroxide in the form of sticks, and then through two or three 
tubes 15 mm in diameter and 25 cm long filled with phosphorus 
pentoxide which had been sublimed in a current of oxygen. When 
not in use these tubes were always sealed, and great care was exer- 
cised to avoid the entrance of moist air from the exits where the 
gases were delivered for use. If the phosphorus pentoxide were to 
become moist on that side there would be danger that the gases 
might carry some of the moisture away with them. 

The electrolytic apparatus containing the sulphuric acid or solu- 
tion of barium hydroxide consisted of a U-tube with platinum 
electrodes. The limbs of the tube were about 35 mm in diameter 
and 55 cm long. It was filled about two-thirds full at first, and 
when the solution became too concentrated, water recently boiled 
and cooled out of contact with the air was introduced through the 
small tube shown on the oxygen side of the apparatus. It was easy 
to do this without allowing any air to enter, but after each filling a 
considerable amount of the gases were generated before further use 
of them for a determination. The water used for preparing the 
original solution and for subsequent dilutions was prepared by 
redistilling distilled water with the addition of an alkaline solution 
of potassium permanganate and collecting the portion that was free 
from ammonia. 

The resistance of the sulphuric acid in the apparatus was 4 to 5 
ohms, while that of the solution of barium hydroxide was consider- 
ably greater. It was necessary to cool the electrolytic apparatus 
with a pretty rapid current of water through the jar containing it 
The electric current used had a pressure of 120 volts and was 
reduced by means of a rheostat placed in series with the electro- 
lytic cell. With the sulphuric acid electrolyte a current up to 15 
amperes could be used, giving 6 liters of hydrogen per hour. With 
the barium hydroxide it was not considered safe to go beyond 4 
liters per hour, because of the greater resistance and consequent 
heating of the solution. 



i8d. Bulletin of the Bureau of Standards, \v6i,4yNo.». 

Copper Oxide. — In the first three series of experiments copper 
oxide was used to convert the hydrogen into water. In the first 
three experiments copper oxide prepared by precipitating copper 
sulphate with a hot solution of sodium hydroxide was used. The 
precipitate was washed by decantation until it became colloidal and 
then washed thoroughly on a Buchner funnel. This oxide retained 
a trace of sulphate which was reduced by the hydrogen to sulphur 
dioxide, and the latter was found in small amount in the water 
obtained. Only two determinations were made with this oxide. 
Seven determinations were made with a sample of copper oxide 
purchased as pure from Kahlbaum. It contained arsenic and other 
impurities. As these determinations formed a part of the first series, 
the results of which are rejected for reasons to be given below, they 
need not be discussed further here. The copper oxide for the 
remainder of the first and for the second and third series was pre- 
pared by precipitation of a hot solution of copper sulphate, Rochelle 
salt, and sodium hydroxide with glucose. The cuprous oxide 
obtained could be washed indefinitely, and all sulphates were very 
completely removed. After ignition in a current of oxygen the 
oxide retained a very small amount of carbon dioxide ; but as this 
appeared as a gas at the end of the experiment and the amount 
could be determined, no serious error can have arisen from this 
source. The same copper oxide was used repeatedly, and after 
several determinations the carbon dioxide nearly disappeared. 

Balance and weights. — ^The balance used was made by Ruprecht, 
of Vienna, and was designed to carry a maximum load of i kilogram 
on each pan. The air of the balance case was dried by means of a 
rapid current of air blown through two wash bottles containing con- 
centrated sulphuric acid and a little chromic anhydride. The spray 
of sulphuric acid carried by the current was removed by passing 
through two tubes, the first containing glass wool and the second 
cotton wool. The current of air was stopped ten to twenty minutes 
before the weight was determined. During the last series of experi- 
ments the balance case was inclosed in a larger glass case and the 
air within the latter was dried by means of large dishes of calcium 
chloride set on top of the inner case. For determinations in which 
the weight of the hydrogen was involved the weight was always 
determined twice at an interval of one-half hour or more and with 



lieyet.} The Atomic Weight of Hydrogen. 185 

the current of air passing into the case during a part of the interval. 
In 100 pairs of weights taken from the notebook at random the 
average difference was 0.05 mg and the maximum difference 
0.12 mg. 

Weights. — ^The weights used were carefully calibrated by Mr. 
Pienkowsky, of this Bureau, at the beginning of the work, a second 
time after they had been in use for ten months, and a third time at 
the completion of the investigation, a little more than two years 
after it was begun. The largest change observed in any of the 
weights used was 0.04 mg, while none of the platinum weights 
changed more than o.oi mg. The aluminum rider gained 0.014 
mg. A recalculation of the amounts of hydrogen in the last series 
showed that the use of the new corrections caused no change 
exceeding 0.14 mg in the weight of the hydrogen for any experi- 
ment of that series, while the algebraic sum of the changes for the 
five experiments of the series was 0.09 mg or i part in 250,000 of 
the weight of hydrogen used. 

The calibration of the weights was of course to a vacuum standard. 
Since the substances to be weighed were always inclosed in a glass 
apparatus whose volume remained constant, and which was counter- 
poised by another glass apparatus of very nearly the same volume 
and weight, no vacuum correction in the ordinary sense was 
required. For our present purpose it is most convenient to assume 
the brass weights in air as standard. If we do this, the platinum 
weights will appear too heavy because they displace less air in pro- 
portion to their weight. This requires a correction of 0.087 °^&> 
which must be added for each gram of platinum weights used. For 
convenience a table was prepared which included this correction for 
the platinum weights with the other corrections, as determined in 
the comparisons of the weights. 

PUfilTY OF THE GASES USED. 

As with all atomic weight determinations, the value of the 
present investigation depends in very large measure upon the purity 
of the substances weighed — in this case, hydrogen, oxygen, and 
water. The impurities which might be present were: In the 
hydrogen, nitrogen, oxygen, water, phosphorus pentoxide, and com- 
pounds of sulphur; in the oxygen there might be the same impuri- 



1 86 Bulletin of the Bureau of Standards, \yoi. 4. no. i. 

ties with hydrogen in place of oxygen; in the water, sulphur dioxide 
or carbon dioxide. 

Nitrogen, — In the former series of determinations there was 
obtained at the end of each experiment a small amount of gas which, 
when calculated as nitrogen, corresponded to about one one-thousandth 
of the weight of hydrogen used. It was found quite early in the 
present investigation that when the water is removed from the 
apparatus containing reduced copper it carries with it a small quan- 
tity of hydrogen, probably hydrogen which has been occluded by the 
copper. The gases were analyzed in a narrow eudiometer of such 
length that when the amount of gas was small the column of mer- 
cury in the eudiometer was 600 to 650 mm in length, so that the 
gas was under a pressure of only about one-seventh of an atmosphere. 
In this way quantities of nitrogen as small as 0.02 mg could be 
measured. 

As will be seen below, it was possible to secure copper oxide so 
pure that only very small amounts of nitrogen were found at the 
close of experiments in which it was used. But the best evidence 
of the freedom of the hydrogen from nitrogen was obtained in 
the last series. From 22.6 g of hydrogen and the equivalent 
amount of oxygen there was obtained only 0.59 mg of nitrogen. 
This includes all of the nitrogen in the oxygen, as well, and all of 
the leakage of the stopcock during seven weeks. If we assume that 
two-thirds of this nitrogen came from the hydrogen, it is only i 
part in 57,000 by weight, or i part in 800,000 by volume. On the 
basis of this evidence it is assumed that all of the hydrogen used 
was free from nitrogen, and no correction has been made for the 
small quantities found in each experiment. It is not believed that 
the error from this source can be so great as i part in 20,000. 

Incidentally these experiments have demonstrated the possibility 
of using, without leakage, ordinary, well-ground, and carefully 
lubricated stopcocks, under such conditions that they are subjected 
to atmospheric pressure with a vacuum inside of the apparatus for 
days together. The well-known rubber lubricant was used. It was 
made by heating a mixture of 16 parts of vaseline, 8 parts of pure 
rubber, and i part of paraffin to a temperature of 350® to 400° for 
several hours until it was thoroughly homogeneous. For warm 



Noyes.^ The Atomic Weight of Hydrogen. 187 

weather, or for a stopcock liable to become warm, a little more 
paraffin was added. 

Oxygen, — After the investigation had progressed so far that it was 
evident that the results difEered from Morley's by a much larger 
amount than can be accounted for by accidental errors, it was feared 
that the hydrogen contained a trace of oxygen which escaped con- 
version into water as the gas passed over the platinized asbestos and 
copper gauze, especially as the latter were heated to only about 
350? To test this possibility the purefied and dried hydrogen was 
passed through a hard glass tube containing platinized asbestos 
heated to dull redness and then through a phosphorous pentoxide 
tube. The latter was closed with stopcocks and was weighed each 
time filled with hydrogen and with the use of a counterpoise. The 
earlier experiments gave appreciable amounts of water (i mg from 
I g of hydrogen), which was in part, at least, from the asbestos, and 
even after the asbestos had been heated almost daily for six weeks 
some water was still obtained (i.i mg from 2.74 g of hydrogen).' 
But when some of the same hydrogen was passed over strips of 
palladium heated to 360° in an electrically heated air bath 3.78 g 
of hydrogen gave a change of weight of —0.08 mg. It still seemed 
possible that a trace of oxygen mixed with dry hydrogen might 
pass the palladium without change. To test this a small T tube 
was introduced between the hydrogen generator and the palladium 
tube in such a manner that the lower arm could be filled with dry 
oxygen. This would then find its way into the hydrogen by slow 
diffusion. The amount of oxygen retained in the arm of the T 
tube was found in two experiments to be 1.68 and 1.94 mg, respec- 
tively, while in three experiments in which similar amounts of 
oxygen were allowed to diffuse into the hydrogen before it entered 
the palladium tube there were found 2.29, 2.21, and 2.58 mg of water. 
While the conditions were such that an exact quantitative agree- 
ment could not be expected the experiments demonstrated that 
minute quantities of oxygen can be readily detected by this method. 

• It seems possible that this water maj have passed through the walls of the red- 
hot tube during the five hours of the experiment. It seems not improbable that 
glass, as a viscous liquid, may dissolve a small amount of water, and that such dis- 
solved water might slowly diffuse through to the inner surface. This question is 
worthy of further study. 



1 88 Bulletin of the Bureau of Standards. [ vot. 4. No. *. 

After the close of the last series of experiments the hydrogen was 
tested by passing it through the tube containing strips of palladium 
heated to 360° and then through the pentoxide tube. In these 
experiments there were passed 2.74, 2.92, and 2.92 g of hydrogen^ 
respectively, while the changes in weight of the phosphorus pen- 
toxide tubes were —0.44, +0.14, and +0.04 mg, quantities scarcely 
beyond the errors of weighing and insignificant in proportion to the 
weight of the hydrogen. 

Water. — The experiments just described demonstrate the absence 
of water in the hydrogen used in the last series. After the close of 
the third series hydrogen from the apparatus was passed through 
the phosphorus pentoxide tube at the rate of 6 liters an hour for five 
successive days, 12.6 g of hydrogen in all. The changes in weight 
of the pentoxide tube were — o.oi, +o-53j —1.06, —0.33, +0.14 
mg; in all a net loss of 0.76 mg, or one part in 17,000. At the 
close of the fourth series 3.78 g of hydrogen were passed through 
the pentoxide tube at the rate of 6 liters an hour with a change in 
weight of —0.04 mg, and a similar amount passed through the tubes 
containing heated palladium gave a change of weight of —0.08 mg. 

It seems, therefore, that the phosphorus pentoxide used to dry the 
hydrogen retained its efficiency to the end. The first of these tubes 
showed considerable deliquescence caused by the water still remaining 
in the hydrogen after it passed the sticks of caustic potash, but the 
last tube showed no sign that it was affected by the moisture. 

Phosphorus Pentoxide. — Morley* has shown that i liter of a gas 
at ordinary temperatures carries with it only 0.00002 m% of vapor 
of phosphorus pentoxide. This would correspond to about 0.0002 
mg in I g of hydrogen, an amount without any significance in 
comparison with the degree of accuracy now possible in determina- 
tions of atomic weights. It is believed that the crystalline phos- 
phorus pentoxide obtained by sublimation, adhering as it did closely 
to the walls of the tube and fibers of glass wool on which it was 
deposited, was much less likely to be carried on mechanically by the 
current of gas than the finely pulverulent pentoxide in its usual 
form would have been. 

Compounds of Sulphur. — After the close of the third series a 
careful test for compounds of sulphur was made by bringing together 

•J. Am. Chem. Soc. 26, p. 1171; 1904. 



Neyes-i The Atomic Weight of Hydrogen. 189 

the hydrogen and oxygen delivered by the apparatus in such a 
manner that they could be burned and the water collected. The 
hydrogen was evolved at the rate of 6 liters an hour, the most rapid 
rate used in the atomic weight determinations. The water obtained 
weighed 11 2.4 g. A little bromine water and 0.1 g of sodium 
carbonate were added to it and it was evaporated to dryness in a 
platinum dish on an electric plate. The residue was acidified with 
hydrochloric acid, filtered from silica which came from the glass 
apparatus in which the gases were burned, and the filtrate was tested 
with a solution of barium chloride. A trifling turbidity appeared 
slowly, estimated to be less than that occasioned by 0.1 mg of sul- 
phuric acid in a solution of similar volume and character. This 
would correspond to i part of sulphur dioxide, by weight, in 250,000 
parts of the hydrogen. 

Purity of the Oxygen, — ^The experiment just described demon- 
strates the practical absence of sulphur in the oxygen. Tests for 
moisture also showed that no amount which cotdd be of significance 
was present. 

Purity of the Water. — ^In the two experiments referred to above, 
in which copper oxide prepared by the precipitation of copper sul- 
phate with sodium hydroxide was used, some sulphur dioxide was 
found. When pure copper oxide was used no evidence of its pres- 
ence was ever obtained. In all experiments in which the sulphuric 
acid electrolyte was used the water was tested with a dilute solution 
of potassium permanganate (i cc = 0.05 mg available O) and with 
N/io barium or sodium hydroxide, with phenol phthalein as an 
indicator. The amounts required never exceeded o.i cc of the per- 
manganate and 0.03 cc of. the N/io alkali, to produce a coloration 
in from 20 to 40 cc of the water. The water of the last two series, 
especially, was frequently tested for hydrogen peroxide, but none 
was found. 

FIRST SERIES. 

This series consisted of twenty experiments. In the earlier experi- 
ments the weight of the hydrogen was determined by the gain in 
weight of a piece of apparatus containing copper oxide, the water 
formed by the oxidation of hydrogen being condensed within the 
same apparatus. The method used will be clear from Fig. i. 



I go Bulletin of the Bureau of Standards. \yoi. 4, ^o. i. 

About 160 g of copper oxide were placed in the part of the appa- 
ratus represented as lying in the electrical air bath. After sealing 
the apparatus at the end designed to collect the water, its volume 
was determined by hydrostatic weighing, and a tube of almost the 
same volume and weight was prepared. The apparatus was then 
placed in the air bath and heated to 400° while it was connected 
with a Sprengel air pump and exhausted. A phosphorus pentoxide 
tube, sealed to the pump, was interposed between the pump and the 
apparatus and also a small McLeod gauge. ^^ The exhaustion was 
carried to the hundred thousandth of an atmosphere, or further, and 
the heating continued for some time. 

For connection with the pump and for other similar connections 
used throughout the work the end of the apparatus was drawn out 
to fit a glass socket connected with the pump. The joint was com- 
pleted by melting a little Khotinsky cement between the parts in 
contact. Such a joint, if properly made, will hold for an indefinite 
length of time against atmospheric pressure without any leakage 
that can be measured. The parts are easily separated by gentle 
warming and cleaned by warming and wiping with cotton, followed 
by a cloth moistened with alcohol. 

After cooling, the apparatus was rinsed with distilled water, 
wiped with a clean cloth, and placed on the balance. The tare and 
weights were placed on the other pan, the current of dry air started 
through the balance case and the weight completed, with the use of 
the rider, on the following day. 

The apparatus was then connected with the source of hydrogen, 
the copper oxide heated to 300° to 350® and hydrogen passed in for 
four to six hours. A coil of small tin pipe conveying cold water 
was placed around the part of the apparatus outside of the air bath 
to condense the water. By means of the rheostat connected with 
the electrolytic apparatus it was easy to regulate the supply of 
hydrogen to correspond with the rate at which it was oxidized by 
the copper oxide. The operation was always stopped before the 

WThe bulb of the gauge had a capacity of about 16.5 cc. To avoid contaminating 
the mercury by contact with india rubber the gauge was sealed below to an upright 
glass tube about 12 mm in diameter. In this was a light, loosely fitting glass 
plunger. By pressing the plunger down the mercury could be easily forced up into 
the gauge for the measurement. 



Aio«.] 



The Atomic Weight of Hydrogen, 



191 







copper oxide was all reduced, and by heating for a short time after 
closing the stopcock the conversion of the hydrogen to water was 
completed. 

After cooling and standing overnight, as before, the weight of 
the hydrogen which had been introduced was determined. The 
apparatus was then connected at A with the apparatus shown in 
Fig. 2, the other end, E, of the apparatus being connected with the 
Sprengel pump. This apparatus was filled 
with phosphorus pentoxide from C to E. 
The end at C is designed to collect the phos- 
phoric acid resulting from the deliquesence 
of the pentoxide, while it is quite necessary 
that the part C D should be directed up and 
not down, as otherwise the sirupy phosphoric 
acid runs down into the unchanged phos- 
phorus pentoxide and seals the tube. The 
apparatus was, of course, previously exhausted 
and weighed. 

After exhausting the connecting tubes by 
means of the pump the bulb F was placed 
in a freezing mixture of ice and sulphuric 
acid, the stopcock B was closed and the stop- 
cock of the copper oxide apparatus opened. 
By passing hot water through the coil of tin 
pipe surrounding the part of the apparatus 
containing the water the latter was easily dis- 
tilled into F in the course of two to four 
hours. By opening B occasionally any per- 
manent gas brought over with the water 
vapor was. allowed to pass on to the pump 
and transferred by means of the latter to the eudiometer, in which the 
gas was analyzed. When permanent gases were allowed to accumu- 
late in F the passage of the water vapor was checked and condensation 
occurred in the connecting tubes. This diflBculty occurred especially 
in the last two series when considerable hydrogen was present, but 
was rarely experienced in the first three series. After the water 
had been transferred to F and the bulb containing the copper had 
been heated to 400° for a short time, the apparatus containing the 
"737-<>7 2 



KJ 



Fig. 2. 



192 Bulletin of the Bureau of Standards. [ voi, 4, No. 2. 

water was removed and replaced by a tube containing phosphorus 
pentoxide and the heating of the apparatus continued for some time 
longer. Only a few milligrams of water were obtained in this 
manner. The apparatus containing the reduced copper was then 
cooled and weighed next morning, the loss of weight as compared 
with the original weight giving the weight of the main portion of 
the oxygen. 

The reduced copper still retains, however, at 400°, either water 
or hydrogen which can not be removed by the process described. 
To obtain this the apparatus was again placed in the electrical air 
bath, heated to 400°, and the copper oxidized as far as possible by 
means of oxygen from the electrolytic apparatus. The water formed 
was then removed by connection with the phosphorus pentoxide 
tube and heating as before. After cooling and weighing, the 
apparatus was now ready for a second experiment. 

In seven determinations of this series the hydrogen was absorbed 
in palladium, and its weight was determined twice, first by the loss 
in weight of the palladium tube and second by the gain in weight 
of the copper oxide tube. The palladium tube was given the form 
shown at A in Fig. 3. The palladium foil was furnished by 
Heraeus. It was 0.05 mm in thickness. Three hundred and sixty 
grams of it were cut into strips 4 cm wide, and these were wound in 
three rolls, which were placed in the tube A. Before use the rolls 
were placed in a hard glass tube and heated to redness in a current 
of oxygen. After placing it in A it was heated for some time in a 
current of hydrogen till thoroughly dry. It was then cooled and 
charged with hydrogen, and when saturated a current of hydrogen 
was passed through the tube for a short time. The tube was 
weighed with a counterpoise and after standing overnight, in the 
same manner as described for the copper oxide tube. 

The arrangement employed for the transfer of the hydrogen to 
the copper oxide tube is shown in Fig. 3. For greater simplicity 
the air baths in which A and B were placed and supported are not 
shown. The tube C was connected with the Sprengel pump. 
After exhaustion of the connecting tubes the connection with the 
pump was cut off by means of a stopcock situated close to the con- 
nection with C. The palladium tube was then slowly heated while 
the copper oxide tube was heated to 350? The pressure in the 



A5?iw.] 



The Atomic Weight of Hydrogen, 



193 



system could be easily followed by means of the shortened manom- 
eter D E. This contained a small amount of air at D but not 
enough to carry the mercury beyond the bend at E when the pres- 
sure in F fell to zero. The heating of A was so regulated that the 
pressure was usually a little below that of the atmosphere, the 
reaction in B proceeding most rapidly under slightly reduced pres- 
sure. The 360 g of palladium absorbed 2.3 g of hydrogen, and of 
this 2 g could be easily expelled at 150° to 160? This amount 




Fig. 3. 

could be transferred from A to B in three to five hours. The rate of 
transfer could be followed by the amount of water condensed in B. 
When enough water had collected the stopcock of the copper oxide 
tube was closed and the palladium was allowed to cool till most of 
the hydrogen in the connecting tubes had been reabsorbed. The 
stopcock of the palladium tube was then closed and the hydrogen in 
the connecting tubes pumped out into a eudiometer and measured. 
This hydrogen varied from 0.02 to 0.14 mg according to the time 
allowed for the palladium to cool. 



194 Bulletin of the Bureau of Standards, \ voi. /. No. 2, 

The twenty experiments of the first series gave for the atomic 
weight of hydrogen, as calculated from the weight of the hydrogen 
and the weight of the oxygen, i.cxDSigdbo.cxxjio, and from the 
weight of the hydrogen and water 1.0082 i±o.cxx)io. This is a 
smaller probable error than has been obtained by any previous 
observer except Keiser and Morley ; but it was found at the close 
of the series that it is subject to a constant error which is 
apparently, about three times the " probable error." 

It was known at the beginning of the investigation that copper 
oxide at 400° would retain a small amount of water. It was hoped, 
however, that this might be made very small and also that by mak- 
ing the end of one experiment the beginning of the next the total 
amount of water retained would be so nearly constant that it would 
not afFect, appreciably, the result of any experiment in the series, 
after the first. At the close of the last experiment of this series it 
was thought wise to test this point by transferring the copper oxide 
to a hard glass tube and heating it in a current of oxygen. To my 
surprise there was obtained j^"],"] mg of water, although the previous 
oxidation and heating at 400° had given only 3.3 mg. If we assume 
this water to have come from the last six experiments of the series 
which formed a continuous set in which the end of one experiment 
was the beginning of the next, the value for the six determinations 
becomes i. 0x5782 as calculated from the hydrogen and oxygen or 
1.00791 as calculated from the hydrogen and water. It was at once 
decided to reject the determinations thus far made, and which had 
taken about a year's time, and to begin a new series in which this 
source or error should be eliminated, if possible. 

SECOND SERIES. HYDROGEN FROM SULPHURIC ACID, WEIGHED TWICE* 

In this series the hydrogen was weighed in palladium and also 
after transfer to the copper oxide tube as described above. In order 
to increase the quantity of hydrogen and reduce the error, after the 
water had been removed and the copper reoxidized, a second quan- 
tity, and in one case a third quantity, of hydrogen was introduced 
and the water removed. Finally the reduced copper was transferred 
to a hard glass tube and oxidized in a current of oxygen, and the 
amount of water formed was determined. The oxygen used was 
partly from the S. S. White Dental Manufacturing Company and 



Noyes.} 



The Atomic Weight of Hydrogen, 



195 



was purified by passing it over red-hot copper oxide and through 
wash bottles containing a solution of sodium hydroxide and over 
phosphorus pentoxide. In some of the experiments electrolytic 
oxygen was used. 

Several experiments were made to determine the amount of water 
taken up by the copper oxide in the transfer to the hard glass tube. 
In a similar manipulation with dry copper oxide there were obtained 
2-63, 1.30, 5.32, and 2.45 mg of water. This would correspond to 
an average error of about i part in 10,000. It has not been thought 
best to apply any correction for this error, partly because of the un- 
certainty in its amount but chiefly because it is probably balanced 
by small errors in the opposite direction, due to the retention of 
water by the copper oxide even after several hours at a red heat in 
a current of oxygen, and to the retention of a trace of water by the 
walls or lubricant of the copper oxide apparatus. There is good 
reason, however, for believing that the error from each of these 
sources is very small. 

Seven determinations were made in this series ; but in one of them 
the weight of the oxygen was lost. The results were as follows: 



Weights of Hydrogen. Second Series. 





QnmaH 
CuO tube 


Grams H 
Pdtube 


MgHin 
Ttube 


Mg H from 
Cu 

0.07 


Cor. H 
CuO 


Cor. H Pd 


Average H 


1 


3.72469 


3.72689 


0.15 


3.72462 


3.72667 


3.72565 


2 


3.80383 


3.80280 


0.17 


0.05 


3.80378 


3.80258 


3.80318 


3 


3.75898 


3.75886 


0.18 


0.10 


3.75888 


3.75858 


3.75873 


4 


2.96309 


2.96357 


0.05 


0.03 


2.96306 


2.96349 


2.96328 


5 


2.11437 


2.11366 


0.08 


0.03 


2.11434 


2.11355 


2.11395 


6 


3.53126 


3.53173 


0.19 


0.04 


3.53122 


3.53150 


3.53136 


7 


3.53963 


3.53982 


0.19 


0.04 


3.53959 


3.53959 


3.53959 



196 



Bulletin of the Bureau of Standards. 

Weights of Oxygen and Water. Second Series. 



\yol,4. No J. 





Qrama O from 
loss of CuO 


MgN 


MgCO, 


Mg water 

by reoxida- 

tlon 


Qrams O 
corrected 


Qrams wmter 


1 

2 
3 

4 
5 
6 
7 


29.56469 
30.16645 
29.81141 
23.49099 

27.99401 
28.05652 


0.76 
0.37 
0.32 
0.13 
0.20 
0.38 
0.24 


0.28 
2.33 
0.79 
0.60 
1.16 
0.89 
0.22 


15.26 
20.25 
23.28 
29.61 
27.65 
36.36 
40.13 


29.57891 
30.18400 
29.83358 
23.51987 

28.02910 
28.09619 


33.30408 
33.98748 
33.59127 
26.48379 
18.89214 
31.56024 
31.63554 



Atomic Weight of Hydrogen. Second Series. 





From H:0 


Prom H : HsO 


1 

2 
3 

4 
5 
6 
7 


1.00765 
1.00800 
1.00792 
1.00792 

1.00791 
1.00785 


1.00767 
1.00799 
1.00795 
1.00790 
1.00795 
1.00792 
1.00786 


Mean, 


1.00787 
db 0.00003 


1.00789 
±0.00003 



Mean of all 1.00788 =b 0.00002 

THIRD SERIES. HYDROGEN FROM SULPHURIC ACID WEIGHED AFTER 
CONVERSION TO WATER BY COPPER OXIDE. 

In this series hydrogen directly from the electrolytic apparatus 
was passed into the copper oxide bulb and converted into water. 
The purpose of the series was more especially to determine whether 
the purity of the hydrogen had been increased by absorption in the 
palladium. The results of the series are not as concordant as those 
of the second, but they indicate that the hydrogen directly from the 
electrolytic apparatus is, if anything, a little lighter, and, presum- 
ably, a little more pure than after it has been absorbed in palladium. 
The results were as follows: 



Noyes,^ 



The Atomic Weight of Hydrogen, 

Weights of Hydrogen and Oxygen. Third Series. 



197 





QnunaHby 
gainofCuo 


H from 
Cu 


QramaH 
corr«cted 


Qrams O bv 
lou of CuO 


MgN 


MgCO, 


BCg water 
by reox- 
idation 


1 

2 
3 
4 
5 


2M2B2 
2.18741 
2.75132 
•4.00068 
4.04061 


0.03 
0.02 
0.03 
0.06 
0.04 


2.44279 
2.18739 
2.75129 
4.00062 
4.04057 


19.34104 
17.33722 
21.80908 

32.04471 


0.16 
0.10 
0.18 

0.17 


0.10 
0.05 
0.05 

0.06 


56.79 
25.98 
34.60 
62.31 
32.41 



Atomic Weight of Hydrogen. Third Series. 



Qrama O corrected Qrams water 



Atomic weight— 



Prom H : O 



Prom H : HsO 



19.39757 
17.36305 
21.84345 

32.07689 



21.84042 
19.55117 
24.59389 
35.75073 
36.11762 

Mean, 



1.00746 
1.00784 
1.00764 

1.00772 



1.00746 
1.00780 
1.00768 
1.00803 
1.00772 



1.00767 
: 0.00006 



1.00774 
db 0.00006 



Mean of all, 1.00771 d= 0.00004 

It will be noticed that the amounts of carbon dioxide found are 
much smaller, owing to the fact that the copper oxide had been 
freed from it by repeated use. The amount of nitrogen was also 
smaller, perhaps because of the simpler manipulations involved. 

FOURTH SERIES. HYDROGEN AND OXYGEN FROM SULPHURIC ACID 
COMBINED BY MEANS OF PALLADIUM. 

With the best manipulation which it has been possible thus far to 
secure, the use of copper oxide involves several sources of small 
constant errors. It is hoped that these errors do not, in the aggre- 
gate, exceed i part in 10,000, but it seemed very desirable to find 
some radically different method which should avoid the use of 
copper oxide. Such a method consists in absorbing hydrogen in 



igS Bulletin of the Bureau of Standards. \^voi. 4, No. 1. 

palladium and converting it into water by means of oxygen. This 
method has already been used by Keiser," but his method of ma- 
nipulation compelled him to use comparatively small amounts of 
hydrogen, and the degree of concordance which he was able to 
secure was not such that his value for the atomic weight of hydrogen 
can be used to decide between Morley's value and that found here. 

The problem seemed at first a very simple one, but several months 
were spent in fruitless experiments before a satisfactory method of 
manipulation was found. 

The 360 grams of palladium foil previously used were placed in a 
somewhat wider tube and were kept from direct contact with the 
glass by means of small glass beads strung on platinum wires. The 
stopcock at one end of the tube was replaced by a tube having a 
capacity of about 50 cc. At the beginning the palladium tube was 
heated and charged with hydrogen and partially exhausted several 
times to remove moisture. It was then heated to 38o°-400° and 
exhausted until the hydrogen showed a residual pressure of 0.50 to 
0.70 mm as measured by the McLeod gauge. At this pressure and 
temperature 360 grams of palladium retain only 2 to 3 mg of hydro- 
gen and the amounts of hydrogen given out for small changes of 
pressure are as follows: 



0.40 


to 


050 


mm, 


0.11 mg H 


0.50 


u 


0.60 


tt 


0.10 " ** 


0.60 


a 


0.70 


tt 


0.094 " " 


0.70 


u 


0.80 


tt 


0.087 " " 


0.80 


tt 


0.90 


tt 


0.080 " " 


0.90 


tt 


1.00 


tt 


0.073 " " 


3.90 


tt 


4.00 


tt . 


0.044 " " 


16.90 


tt 


17.00 


tt 


0.020 " " 



A change of temperature of 10° for pressures less than i mm corre- 
sponds to a change of 0.03 mg in the amount of hydrogen retained. 
At the end of an experiment it was easy to bring the apparatus to a 
condition of temperature and pressure closely approximating that 
at the beginning, and by means of the table a correction of sufficient 
accuracy could be applied. 

After exhausting and measuring the temperature and pressure as 
described, the apparatus was allowed to cool, rinsed with distilled 

"Am. Chem. J., 18, p. 354; 1888. 



Ai9«.] The Atomic Weight of Hydrogen. 199 

water, wiped, placed on the balance, and on the following morning it 
was weighed. It was then charged with hydrogen (about 2.3 grams) 
and weighed again on the morning of the third day. The apparatus 
was then connected with the oxygen side of the electrolytic gener- 
ator. The palladium tube was inclined so that the water formed ran 
down into the receptacle at the end. The oxygen entered rapidly 
for a few minutes, but the heat generated soon caused the pressure 
of the hydrogen to increase and check the current. The oxygen 
then continued to enter slowly, with the stopcock partly closed, for 
two or three hours. After that the rate at which the oxygen was 
taken changed quite suddenly, so suddenly that the first time the 
experiment was tried the electrolyte was drawn over and the elec- 
trolytic apparatus was broken. From this time to the end the en- 
trance of the oxygen was regulated by the stopcock and was allowed 
to enter as rapidly as it was thought desirable to run the generator. 
More than enough oxygen to combine with the hydrogen present 
was easily introduced. On the fourth day, after weighing, the 
apparatus was charged again with hydrogen. 

On the fifth day the manipulation varied. In some cases oxygen 
was admitted in excess as on the third day. In other cases, as the 
end of the oxidation of the hydrogen approached, the apparatus was 
weighed roughly at intervals and the admission of the oxygen was 
stopped while 5 to 10 mg of hydrogen remained unoxidized. By 
this method of manipulation a day was saved. On the sixth day, 
when an excess of oxygen was admitted on the fifth, a small excess 
of hydrogen was admitted. It was necessary to wait till the follow- 
ing day before weighing. 

On the sixth or seventh day, according to the method of manipu- 
lation chosen, the water and excess of hydrogen were removed and 
the apparatus brought back to a condition for the beginning of 
a new experiment. A receptacle similar to that described above 
was xised for the water. On account of the hydrogen which 
accumulated rapidly in the bulb with the water and stopped the 
current of water vapor, it was found desirable to give the bulb a 
capacity of about 100 cc. Any nitrogen present was, of course, 
carried over with the first portions of the water vapor and hydrogen 
and this part of the gas was collected and analyzed separately. At 
the close of the removal of the water the receptacle for the water 
was replaced by a phosphorus pentoxide tube which permitted of a 



200 



Bulletin of the Bureau of Standards, 



[Vol. 4. I^o. i. 



free connection between the palladium tube and the pump for the 
measurement of the residual pressure. It was necessary to heat 
the palladium tube at least two hours in the electrical air bath to 
secure constant conditions for the measurement of the residual 
pressure. This was not understood in the earlier determinations 
of this series and may be one reason why some of the results are 
not very satisfactory. 

In the results which follow the amounts of nitrogen and carbon 
dioxide are given as an indication of the magnitude of the errors 
which may have been occasioned by traces of these gases or by 
leakages, but no correction for these gases has been applied. 

Theoretically, the weight of the apparatus at the end of an experi- 
ment should be the same as at the beginning. Practically, it was 
almost always heavier because of the retention of a small amount 
of water. When the hydrogen was allowed to accumulate in the 
receptacle for water the moisture would condense in the connecting 
tubes and stopcocks, and if allowed to remain for a short time in 
contact with the lubricant of the stopcock could not be entirely 
removed. In some cases minute drops of water could be seen within 
the bore of the stopcock, and these would not evaporate during any 
reasonable length of time. The gain in weight of the apparatus 
during the experiment was, accordingly, assumed to be due to water 
which had been retained and was added to the weight of water 
found directly. In cases where condensation was avoided the 
amount of water was very small or even became negative. (See the 
following series.) 

Weights of Hydrogen and Oxygen. Fourth Series. 



1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 



Grains H 



. 2.31840 
4.13630 
4.18248 
4.19599 
2.31593 
4.60148 
4.63931 
4.57292 



Ms cor. for 

chang^eB of 

t and P. 



—0.05 
—0.06 
+0.24 
—0.51 
—0.01 
—0.23 
-f0.14 
4-0.18 



MgH 
recovered 



39.19 
8.90 
7.16 
2.02 
8.46 
4.33 
3.20 
0.36 



Grama H 
corrected 



2.27916 
4.12734 
4.17556 
4.19346 
2.30746 
4.59692 
4.63625 
4.57274 



MffN 


MffCO, 


0.48 


0.02 


0.50 


.... 


0.52 


0.02 


0.15 


0.16 


0.11 


0.08 


0.07 


0.07 


0.02 


0.28 



Grama O 

18.08455 
32.76527 
33.13449 
33.27384 
18.30863 
36.48543 
36.79354 
36.28696 



Ai9«.l 



The Atomic Weight of Hydrogen. 

Weights of Water and Atomic Weight of Hydrogen. 



20I 





Qramaof 
water 


Mg water 

retained 


Grama water 
corrected 


Atomic weight— 




Prom H : O 


Prom H : H,0 


1 


20.29807 


63.21 


20.36128 


1.00823 


1.00830 


2 


36.87182 


18.61 


36.89043 


1.00774 


1.00780 


3 


37.30667 


1.20 


37.30787 


1.00818 


1.00821 


4 


37.46202 


2.51 


37.46453 


1.00822 


1.00831 


5 


20.61671 


-3.14 


20.61357 


1.00825 


1.00839 


6 


41.07653 


5.09 


41.08162 


1.00795 


1.00797 


7 


41.41452 


14.53 


41.42905 


1.00806 


1.00808 


8 


40.85460 


3.74 


40.85834 
Mean, 


1.00813 


1.00817 




1.00809 


1.00815 










±0.00004 


±0.00005 








Mean of all, 


1.00812 


±0.00003 



FIFTH SERIES. HYDROGEN AIYD OXYGEN FROM BARIUM HYDROXIDE COM- 
BINED BY MEANS OF PALLADIUM. 

The manipulation in this series was essentially the same as in the 
fourth series. The series has much greater value than the former 
one, partly as shown by the concordance of the results, partly 
because the processes of manipulation had been more thoroughly 
mastered, and partly because the electrolyte used gives a greater 
probability of purity for the hydrogen. In those experiments in 
which oxygen was introduced last a small quantity was left in the 
bore of the three-way stopcock and was usually found in the subse- 
quent analysis of the first portions of gas removed. In one experi- 
ment of this series only one-half the quantity of hydrogen was used 
and too much oxygen was admitted by mistake. This so compli- 
cated the manipulation that the experiment was unsatisfactory and 
it has been omitted from the table. It gave the values 1.008 14 and 
1.00823. 



202 



Bulletin of the Bureau of Standards. 

Weights of Hydrogen and Oxygen. Fifth Series. 



\yol.4.No.3, 





Qrams H 


Mg cor. for 
change 
to and P 


MgH 
recovered 


Qrama H 
corrected 


MgN 


MgCO, 


MgO 


Grams O 


1 


4.61443 


-0.07 


2.56 


4.61180 


0.11 


0.17 




36.60909 


2 


4.62877 





5.19 


4.62358 


0.08 


0.03 


0.13 


36,69575 


3 


4.60386 


-0.02 


5.31 


4.59853 


0.22 





1.31 


36.50484 


4 


4.56300 


+0.04 


4.72 


4.55832 


0.06 





0.29 


36.17887 


5 


4.21188 


—0.04 


7.85 


4.20399 


..u 





0.11 


33.37000 



Wdghts of Water and Atomic Weight of Hydrogen. 





Qrama water 


Water 
retained 

1.71 


Grama water 
corrected 


Atomic weight— 




From H : O 


From H : H^O 


1 


41.21934 


41.22105 


1.00779 


1.00779 


2 


41.30740 


9.07 


41.31647 


1.00798 


1.00806 


3 


41.09872 


3.40 


41.10212 


1.00776 


1.00780 


4 


40.74186 


-2.82 


40.73904 


1.00795 


1.00790 


5 


37.56732 


6.04 


37.57336 
Mean, 


1.00782 


1.00786 




1.00786 


1.00788 










3:0.00003 


±0.00003 








Mean of all, 


1.00787 


=b0.00002 



The mean of the four series, giving them equal weight, is 1.00787 
from the hydrogen and oxygen and i. 00791 from the hydrogen 
and water. The second and fifth series have, however, much 
greater weight than the third and fourth, and when we consider, 
further, that there was probably a trifling loss of water, especially 
in the third series, the value 1.00787 seems to be the most probable 
result which can be calculated from the work. 

It has seemed of interest to recalculate Morley's results on the 
oxygen basis for comparison with the result here given. 



^'oyes.] The Atomic Weight of Hydrogen, 203 

Atomic Wdght of Hydrogen. Morley's Results. 

1 1.00765 1.00778 

2 1.00751 1.00766 

3 1.00768 1.00774 

4 1.00755 

5 1.00773 1.00750 

6 1.00773 1.00778 

7 1.00777 1.00786 

8 1.00764 1.00761 

9 1.00759 1.00752 

10 1.00752 1.00737 

11 1.00746 1.00734 

12 1.00744 1.00771 



Mean, 1.00761 1.00763 

+0.00002 dbO.00003 

Mean of all, 1.00762 dbO.00002 

The difference between this result and that given above is greater 
than can be accounted for on the basis of accidental errors. While 
the average of the results of the best determinations by other observ- 
ers approaches more nearly to the result of this investigation than 
to Morley's value, it does not seem justifiable to calculate a mean on 
such a basis. For reasons which will be given in a later paper the 
most probable value which we can get at the present time seems to 
be the average between Morley's value and that here given. That 
average is 1.00775. Morley's value and my own each differ from 
this by one part in 8,cxx). 

CBAUGE IN WEIGHT OF THE HYDROGEN WHEN CONVERTED INTO WATER. 

As was stated in the introduction, one purpose of this investiga- 
tion was to secure, if possible, some evidence of a change of weight 
which might occur in a reaction in which a large amount of energy 
is dissipated. In twenty-five experiments the same hydrogen was 
weighed, first, as absorbed in palladium and, second, after conversion 
into water by means of the copper oxide. The results were as 
follows: 



204 



Bulletin of the Bureau of Standards. 



\Vol.4.No.2, 



Qain of CuO 


LOBB of Pd 


DliT. Mff ^ 


Gain of CuO 


Lobs of Pd 


Difr. VL% 


1.04216 


1.04295 


-fO.79 


0.95151 


0.95207 


+0.56 


1.46493 


1.46642 


-fl.49 


1.98130 


1.98053 


-0.77 


0.96114 


0.96231 


-f-1.17 


1.82248 


1.82205 


-0.43 


1.51279 


1.51296 


+0.17 


2.04840 


2.04816 


-0.24 


1.17961 


1.17973 


-f0.12 


1.71048 


1.71042 


-0.06 


1.22273 


1.22268 


-0.05 


1.96621 


1.96648 


+0.22 


1.13563 


1.13541 


-0.22 


0.99685 


0.99707 


+0.22 


1.30184 


1.30150 


-0.34 


2.11434 


2.11335 


-0.79 


1.22851 


1.22699 


-1.52 


2.20439 


2.20472 


+0.33 


0.99563 


0.99600 


+0.37 


1.32683 


1.32678 


-0.05 


1.24243 


1.24270 


+0.27 


2.07207 


2.07281 


+0.74 


1.24639 


1.24754 
1.52706 


+1.15 
+0.24 


1.46752 


1.46678 


-0.74 


1.52682 


36.72299 g 


36.72562 g 


+2.63mg 



An examination of these results show that in fourteen experiments 
the hydrogen as weighed in the palladium appeared heavier, while 
in eleven experiments the hydrogen after conversion into water 
appeared heavier. The average difiference between the two weights 
of a given quantity of hydrogen was 0.52 mg or i part in 3,000, while 
the average amount by which the hydrogen as weighed in the pal- 
ladium appeared heavier was o.i i mg or i part in 14,000. It is clear 
that these results do not justify any conclusion either way with 
regard to a change in weight of the hydrogen during the reaction 
other than that if any change of weight occurs it must be very 
small. It seems scarcely possible that a change of so much as i 
part in 10,000 of the weight of the hydrogen takes place. It is^ 
possibly, of interest to note that so far as the results furnish any 
indication whatever they point toward a trifling loss of weight, a 
result which would agree with Landolt's elaborate study of the 
question." It is hoped that this problem may be taken up again by 
a method capable of giving more accurate results. 

Washington, September 11, 1907. 

"Zs. physik. Chem. 55, p. 589. 



ON THE BEST METHOD OF DEMAGNETIZING IRON 
IN MAGNETIC TESTING. 



By Charles W. Burrows. 



The magnetic permeability of a specimen of iron is a function of 
its previous mechanical, thermal, and magnetic history as well as of 
its chemical composition. While therefore the magnetic permeabil- 
ity of a given piece of metal may be measured quite accurately at a 
given instant, in general the very process of measurement adds a 
new chapter to the history of the metal and may leave it with mag- 
netic properties different from those it had at the beginning of the 
test. Such a test may be quite misleading as regards the real mag- 
netic properties of the specimen. Hence we are most concerned 
with those properties and conditions that can be associated and 
reproduced. Some little space will therefore be devoted to the con- 
sideration of the after effects of various details in the history of the 
magnetic substance, and a plan will be outlined whereby a specimen 
may be freed from all effects of previous magnetic treatment, and so 
be brought to a standard condition. We shall thus define a set of 
normal conditions and specifications under which the specimen is to 
be tested. When this is done, the permeability becomes a definite 
physical constant, and may be redetermined at will. All numerical 
quantities and equations are given in the electromagnetic c. g. s. 
system of units. Field strength and induction per square centimeter 
are expressed as so many unitSy although many writers prefer the 
more distinctive term gauss. 

THE SSSULTS OF EARLIER OBSERVERS. 

Considerable work on the influence of previous magnetic treat- 
ment and certain other related details on the value of the induction 
has been done and some of the more important conclusions are here 

205 



2o6 Bulletin of the Bureau of Standards, \,vol 4. a'o. ^- 

given. Ewing in his classic work " Magnetic Induction in Iron and 
other Metals," third edition, 1900, has recorded the following phe- 
nomena, most of which are founded on magnetometric measurements 
either by himself or by earlier investigators. 

(i) Demagnetization by hand reyersals or by rotating commutator 
is complete if the maximum current is at least as great as the greatest 
used since the last demagnetization.^ 

(2) If a force is repeatedly applied and removed, the values of the 
induction and the residual magnetism form two increasing sequences 
of numbers whose last terms approach each other." This has been 
called "molecular accommodation." 

(3) During repeated reversals of the same magnetizing force, the 
change of induction on reversal gradually becomes smaller and 
finally reaches a constant value.' 

(4) After the change of induction on slow reversal of current has 
become constant, a sudden reversal will at first increase the change 
of induction on reversal, but later reversals make this change smaller 
than ever.' 

(5) After application of an intense magnetizing force the tendency 
to a diminution of the change of induction on repeated reversal of 
a given magnetizing force has disappeared.* 

(6) " Creeping " produces a greater induction than is at first shown 
on the application of the magnetizing force. "^ 

In an article entitled " Studies in Magnetic Testing," * Professor 
Searle gives the results of an extended investigation carried out at 
the Cavendish I^aboratory. An alternating current of 90 cycles 
controlled by a liquid rheostat furnished the demagnetizing force. 
Inductions were measured ballistically. The specimens used were 
samples of transformer iron 4 cm wide, 68.8 cm long, and about 
0.035 ^^ thick, and were so arranged that the magnetic circuit was 

* Magnetic Induction, etc., p. 46. 

"Fromme, Pogg. Ann. Ergbd., 7; 1875. Wied. Ann., 4; 1878. 

' Magnetic Induction, etc., p. 340. My experience seems to indicate that this later 
decrease is nothing more than a part of the origrinal decrease accelerated perhaps by 
the sudden reversal. 

* Magnetic Induction, etc., p. 341. This does not accord with my experience, and 
is therefore probably found only in certain specimens. 

* Ewing, Phil. Trans., p. 569, 1885. 

•G. F. C. Searle, Proc. of Inst, of Elect. Engrs., Part 170, 84, pp. 55-118; 1904. 



Burrows.] Method of Demagnetizing Iron. 207 

a square about 50 cm on a side. The more important conclusions 
of this paper are here given. 

(i) Complete demagnetization is obtained by an alternating 
current with a frequency of 90 cycles per second, provided the 
initial demagnetizing force is greater than a certain ** critical 
value." 

(2) An imperfect demagnetization results in a lower apparent 
induction. 

(3) The effect of many reversals of a force Hy on the apparent 
induction due to a small force H= i is modified by many reversals 
of a force H^ as follows: 

(a) If Hg^ is as large as the critical value, it wipes out the effect of 
Hy and leaves its own after effect. 

(b) If Hy. is less than the critical value its effect in raising the 
apparent induction is less as Hy is greater. In every case it leaves 
its own after effect. 

(c) If H^ is ver>' small, less than one, the after effect in certain 
cases is to give a lower apparent induction than if H^ were omitted.' 

(d) li Hy = o the apparent induction may be raised by a small 
value of /4. ' 

(4) Many reversals of a force H^. cause a lowering of the apparent 
induction due to a smaller force H^^ and the lowering increases with 

(5) A constant force superposed upon the force used in determin- 
ing the induction reduces the apparent induction. A constant force 
of H=o,2 in one case caused a 20 per cent reduction for low values 
of A* 

(6) Virgin iron gives lower values of the apparent induction than 
demagnetized iron in the lower values of B. In the upper regions 
the difference disappears. This iron, although it is called virgin 
because it had experienced no other magnetizing force than the 

^ I have not attempted to verify this. It seems analogous to the decrease in appa- 
rent induction noted in some cases when the upper limit of the demagnetizing force 
was too low. 

•This is contrary to my experience. 

*I have noticed a lowering of the apparent induction when the specimen was 
turned so that the earth's field was parallel to its length. 
11737—07 3 



2o8 Bulletin of the Bureau of Standards, \ voi. 4. No. 2. 

earth's field, showed a small initial induction even after careful 
annealing. ^'^ 

All of the above conclusions have been carefully examined during 
the present investigation and have been verified except in certain 
cases, particularly that on the efiiciency of demagnetization by alter- 
nating current, which will be discussed latter. While these general 
conclusions do not cover exactly the same ground as the present 
work yet, with an exception or two, there are no inconsistencies 
between the earlier work and my own. 

DBFimXIONS. 

In Fig. I, B and H are the magnetic induction per square cen- 
timeter and magnetizing force, respectively. Then if we start with 
a piece of virgin iron and apply successively increasing magnetizing 
forces and note the corresponding inductions, we get a series of 
points having the line OA as locus. If the magnetizing forces had 
been negative instead of positive, the symetrical curve OB would 
have been traced. The positive branch of the curve is commonly 
called the ascending B-H curve, or simply the ascending curve. 
Consider the point A on the ascending curve and the corresponding 
point B on the negative curve. In the course of the ascending 
curve let the magnetizing force be reversed at the point A. This will 
cause the point which represents the magnetic state of the iron, or 
state point, to move along the curve ARB' where B' in general is a 
different point from B. Another reversal will trace the curve B'R'A' 
where also A' is different from A. If the magnetizing force is 
reversed many times, the path of the state point eventually becomes 
a closed curve such as is pictured in Fig. 2. The upper tip of 
this curve defines a pair of values of B and H, If other loops are 
traced in this manner, but so that each succeeding loop is larger than 
its predecessor, the locus of the tips of the loops forms the normal 
curve of ascending reversals, or, as it is sometimes called, the com- 
mutation curve. The locus of the lower tips of these same loops is 
a curve symmetric with this. 

*° I have not been able to obtain any iron free from initial polarization and con- 
sequently have no data for virgin iron. The experiment cited is not conclusive, as 
the small residual magnetization detected would tend to produce the same effect 
attributed to the fact that the iron is in the virgin state. 



Surrows.} 



Method of Demagnetizing Iron, 



209 



Instead of starting with a piece of virgin iron, or with a piece of 
iron which had been thoroughly freed from all previous polarization, 
we may start with a specimen which has a residual induction repre- 
sented by the point P which obviously could lie anywhere on the 
line RR'. Proceeding as before, we get a system of curves analogous 
to the preceding but with the symmetry lost The point corre- 
sponding to the center of symmetry has been displaced towards P. 




Fig. 1. — Ideal curve to illustrate the d^mithns 0/ magnetic properties, 

Fig. 2. — Ideal curve to illustrate the effect of previous magnetic history on the initial permeability 
of apparently neutral iron. 

This new center may be so far displaced from the origin that on 
reversals of small values of 1/ the induction does not change sign, 
but oscillates between two values of the same sign, such as those 
represented by P' and P". In such a case as this the applied mag- 
netizing force does not determine the absolute induction but only 



2IO Bulletin of the Bureau of Standards, ivoi. /, No. 2. 

the amplitude of the oscillation. Instead of comparing the absolute 
values of B with H^ we should rather compare with H the value 
of this oscillation which is expressible as 

UBn-B.u) 

In order to avoid circumlocution and ambiguity the following 
definitions seem desirable. 

The magnetic induction is one-half the change of magnetic flux 
per square centimeter observed on the reversal of a given magnetic 
force, or 

\ {B^-B_„) 

Permeability is the ratio of this induction to the corresponding 
magnetizing force, or 

B 

The differential permeability is the ratio of an infinitesimal 
change in ^ to the corresponding change in H, Geometrically it 
is the tangent of the angle which the tangent to the curve makes 
with the H axis. 

The hysteresis loop is the path traced by the state point on a 
double reversal of a given magnetizing force after sufficient repeti- 
tion has made the path cyclic. 

A normal hysteresis cycle is one which is symmetrical about the 
origin. The induction and permeability are normal or apparent 
according as the corresponding hysteresis loops are normal or not." 

Iron is in a neutral state when it exerts no external field and 
yields as readily to a positive magnetizing force as to a negative 
one. 

APPARATUS. 

In these experiments the magnetic circuit usually consisted of 
two specimens about 50 centimeters long placed side by side with 
their adjacent ends joined by suitable wrought-iron yokes. The 

"The distinction between "normal" and "apparent" is due to Searle (loc. cit.). 
Rowland (Physical Papers, p. 44) uses "normal" in the sense of "virgin." 



Burrows.] 



Method of Demagnetizing Iron, 



211 



magnetizing coils consisted of two sections, each 40 centimeters 
long, wound with a single layer of 400 turns of No. 22 double cotton 
covered magnet wire. The secondary coil was uniformly distributed 
over the middle portion of the specimen. The shearing correction 
due to end effects is small and has been allowed for in the results. 
The reduction to absolute values, as well as other details of manipu- 
lation, will be described in a subsequent paper. The nature and 
dimensions of the specimens used are shown in Table I. For each 

TABLE I. 

Showing the physical constants of the specimens used in this work. 



specimen 


1 

Length ! Breadth 


Thick. 

nesa 


Diame- 
ter 


Croaa 
section 


Speciiic re- 
sistance in 
micro-ohms 


Transfoniier iron 


51.0 I 1.006 

51.0 1.00 

47.1 


*.0355 
.065 


.578 
.578 


.0357 
.065 
.262 
.262 


14.0 


Q^in 11^4)11 iron 


13.9 


Low carbon steel 


13.4 


Hi^h carbon steel 


45.8 . . . 




18.9 












* Calculated from mass and density. 

kind of iron and steel two specimens were cut from the same rod or 
sheet, and though cut from adjoining parts show a small difference 
magnetically. 

CRITERION OF PERFECT DEMAGNETIZATION. 

In order to reduce iron to a magnetically neutral state, it must be 
freed from the effects of previous magnetization. It must not only 
be freed from all evidences of polarization which would produce an 
external field and which would be indicated by a suspended magnet 
or a movable test coil, but also from all internal polarizations which 
produce no external field. A test coil shows the integrated value of 
the induction and therefore does not show whether the specimen is 
in the neutral state. The specimen may be magnetically homo- 
geneous with no external field and yet not be in the neutral state. 
This appears from Fig. 2. I^et the state point be the origin. If 
the iron is neutral, a small positive force will cause the state point 
to move along the solid line OA tracing the ascending curve. If, 



212 Bulletin of the Bureau of Standards, [Voi. /, No. 2. 

however, the iron has been previously carried along the path OABO, 
the state point is again at the origin, but the iron is so influenced 
by its recent treatment that a small positive force carries the point 
along the path OC, which initially is above the normal path OA. 
Again let it be carried along the path OABA'DO. Once more it is 
at the origin, but with a tendency to move along the path OE with 
increase of H. This latter path is below the normal path. And so 
on, with various preliminary paths for the state points, we could 
cause it to leave the origin in an infinite number of directions which 
would mean an infinite number of initial permeabilities. And yet 
in each of these cases an external magnet or a movable test coil 
would give no indication of the inherited tendencies of the specimen. 

In general, if the origin is made the lower tip of a secondary hys- 
teresis loop, its initial permeability in the ascending curve is less 
than normal. If, however, the origin is near the middle of the 
ascending branch of a secondary hysteresis loop, the initial permea- 
bility is greater than normal. These facts show that the ordinar}^ 
criteria for perfect demagnetization are unsatisfactory and indicate 
that no test is possible which will not modify the neutral state if it 
should exist. 

Before a satisfactory criterion of perfect demagnetization can be 
determined upori, it is necessar^*^ to know something of the nature 
of the influence a residual induction has on the apparent induction. 
With this in view, the following experiment was carried out: A 
specimen was demagnetized as thoroughly as might be and its 
apparent induction measured. Then the specimen was subjected 
momentarily to a magnetizing force which would give it a certain 
residual induction. After the removal of this force the apparent 
induction for the same force as before was determined. These 
operations were repeated with successively increasing polarizing 
forces. The results are shown graphically in Fig. 7. From this 
curve it is seen that as the polarizing force increases the result- 
ant induction decreases. Applied to Fig. i, this means that the 
small cyclic loop P'P P" becomes more nearly parallel to the H 
axis as P recedes from this axis. In consequence of this fact, which 
holds in every case examined, the criterion of perfect defnagnetiza- 
tion is that the induction shall be a maximtun. 



Burrows.] Mcthod of Demagnetizing Iron, 213 

PREVIOUS METHODS OF DEMAGNETIZATION. 

Many methods have been employed to remove residual polariza- 
tions and to reduce the specimen to a magnetically neutral state. 
The method most generally employed is that of descending reversals 
in which the demagnetizing force is repeatedly reversed while it is 
gradually decreased in value. The reversals may be made by hand 
with an ordinar>^ reversing switch, by a rotating commutator driven 
either by hand or by power, or by an alternating current. The 
reduction of current may be made by any form of rheostat. The 
liquid resistance has found favor in many quarters, chiefly because 
it gives a continuous variation of current and not a series of steps, 
as in most types of rheostats. 

Ewing" suggests ^. potential slide^ made as follows: A tall glass 
jar is filled with a dilute solution of zinc sulphate. Three blocks of 
amalgamated zinc are fitted in the jar — one lying on the bottom, one 
fixed at the top, and the third hung between them by a cord, which 
passes over a pulley above to a little winch. The batter}- is con- 
nected to the fixed blocks, and the magnetizing coils to one fixed 
block and to the movable block. By altering the position of the 
movable zinc block the electromotive force applied to the magnet- 
izing coils may be varied. Reversals were made by a rotating com- 
mutator worked by hand. 

Searle " used an alternating current of 90 cycles supplied from the 
city mains. His resistance consisted of a narrow glass trough con- 
taining dilute copper sulphate solution, and furnished with two 
copper electrodes, one of which was movable. By tilting the trough 
so that one end was dry the current could be reduced to a very small 

value. 

CURRENT REGULATION. 

In this investigation all the available methods of current control 
were tried. Several kinds of liquid resistances were used. In some 
of these the electrodes were moved apart so as to give a longer path 
through the liquid. In others the liquid was removed from the 
containing vessel. This was accomplished in several ways — by tilt- 
ing the vessel, by siphoning off the liquid to another vessel, and 
again by allowing the liquid to run out through a stopcock in the 

"Magnetic Induction, etc., p. 44. • 

"Proc. Inst, of Elect. Engrs., 84, p. 61; 1904. 



214 Bulletin of the Bureau of Standards, \vol 4, No. i. 

bottom of a tall cylindrical vessel. The latter was the most satis- 
factory of the liquid type. The ordinary forms of rheostats, with 
fixed steps, controlled by dial sliding contacts, by plugs, or by links 
and mercury cups, were tried. Another form used was the Kelvin 
rheostat, in which the wire is wound from a drum of conducting 
material to an insulating drum. This gives uniform variation, and 
is easily controlled, but is laborious. The most satisfactory rheostat 
used was a cylinder of slate wound with bare wire, having a sliding 
contact moving parallel to the axis of the cylinder. Several of 
these resistances of different sizes of wire are connected in series 
and are highly satisfactory. 

Current decrease was also effected by changing the applied electro- 
motive force while keeping the resistance constant. In this case 
the demagnetizing circuit was connected to two points of an adjust- 
able resistance through which a current was flowing. This method 
was found to offer no advantage over the preceding, but has some 
obvious disadvantages. 

Early in the investigation it became apparent that the efficiency 
of demagnetization depended not so much on the total time con- 
sumed as on the rate at which the demagnetizing current was 
reduced. To test this point the demagnetizing current was reduced 
successively in three different ways. First, so that the rate of 
increase of resistance was constant; second, so that the rate of 
decrease of current was approximately constant, and, third, so that 
the rate of decrease of induction was constant. This last method 
gave the best results and has been followed in all the later work. 

The electromotive force to be used is detennined largely by the 
requirements of the induction measurements to be made after the 
demagnetization. For these the first requirement is constancy, 
which is best obtained by a storage battery furnishing no other 
current. A relatively high voltage is advantageous, because the 
higher the regulating resistance the easier is the regulation and the 
lower the time constant of the circuit. These two factors are 
closely connected with rapidity of the measurements and the accu- 
racy of results. On the other hand, a low voltage means less trouble 
from arcing at the commutator and less outlay for batterj^ and the 
extra resistance needed. Twenty volts is an intermediate value, 
which meets all requirements and has been used in this series of 
experiments. 



Burrows.] 



Method of Demagnetizing Iron, 
POLARIZATION EFFECT. 



215 



It is well at the outset to determine something of the nature of 
the polarization effects which are to be removed by the process of 
demagnetization. To this end several specimens of iron were exam- 
ined after having been exposed to different magnetic treatments. 
The iron was first demagnetized as well as might be and its apparent 
induction determined for a series of values of the magnetizing force. 
Then the iron was subjected to a strong magnetizing force of 100 
units (gausses) after which the induction was redetermined. This 
polarizing force was applied and removed several times, but it was 
not reversed in this first comparison. The results of this experi- 
ment are shown numerically in Tables II, III, IV, and V, and 

TABLE II. 

To illustrate the effect of the residual polarization due to a force of 100 on 
the apparent induction in annealed transformer iron. 



Ifaffnetisins 
force 


Induction 
after demagneti- 
sation 


Apparent 

induction when 

polarized 


Polarization 
effect 


Per cent 

polarization 

effect 


B 


.1 


68 


26 


42 


62 


680 


.2 


192 


67 


125 


65 


960 


.3 


370 


130 


240 


65 


1260 


.4 


670 


230 


440 


66 


1670 


.5 


1290 


480 


810 


63 


2580 


.6 


1680 


720 


960 


57 


2800 


.7 


2570 


1380 


1190 


46 


3670 


.8 


3370 


2510 


860 


26 


4210 


.9 


4300 


3700 


600 


14 


4780 


1.0 


5130 


4750 


380 


7 


5130 


1.1 


5710 


5360 


350 


6 


5170 


1.2 


6730 


6490 


240 


4 


5230 


1.3 


6880 


6750 


130 


2 


5290 


2.0 


8880 


8880 








4440 


3.0 


10750 


10750 








3580 


5.0 


12750 


12750 








2550 


10.0 


14620 


14620 








1460 


15.0 


15280 


15280 








1020 



Plotted in Fig. 3. 



2l6 



Bulletin of the Bureau of Standards. 
TABLE III. 



[ Vol. #. No. 2. 



To illustrate the effect of the residual polarization due to a force of 100 on 
the apparent induction m common sheet iron. 



Magnetizing 
force 


Induction 
after demagneti- 
zation 


Apparent 

induction wrhen 

polarized 


Polarization 
effect 


Per cent 

polarization 

effect 


B 


1 
2 
3 
5 

7 
10 
15 


263 

1314 

3770 

7890 

10270 

12170 

13610 


97 

496 

3130 

7730 

10130 

12160 

13610 


166 
818 
640 
160 
140 
10 



63 
62 
17 
2 
1 




263 
657 
1257 
1580 
1467 
1217 
907 



Plotted in Fig. 5. 



TABLE IV. 



To illustrate the effect of the residual polarization due to a force of 100 on 
the apparent induction in low carbon Bessemer steel. 



Magnetizing 
force 


Induction 
after demagneti- 
zation 

190 


Apparent 

induction when 

polarized 


Polarization 
effect 


Per cent 

polarization 

effect 


B 


1 


90 


100 


53 


190 


2 


680 


370 


310 


46 


340 


3 


1930 


1460 


470 


24 


640 


4 


4150 


3670 


480 


12 


1040 


5 


6790 


6300 


490 


7 


1360 


7 


9990 


9740 


250 


3 


1440 


10 


12470 


12470 








1250 


15 


14170 


14170 








940 



Plotted in Fig. 4. 

graphically in Figs. 3, 5, 4, and 6. From these data and curves 
it is to be noted that the four specimens of iron show several com- 
mon characteristics. 

(i) The induction after demagnetization is greater than the appar- 
ent induction after the intense polarization. The difference between 



BnrTows.] 



Method of DemagneAizing Iron, 
TABLE V. 



217 



To illustrate the effect of the residual polarization due to a force of 100 on 
the apparent induction in high carbon crucible steel. 



Magnetising 
force 


Induction 
after demagneti- 
zation 


Apparent 

induction when 

polarized 


Polarization 
effect 


Per cent 

polarization 

effect 


B 


1 


108 


54 


54 


50 


108 


2 


249 


125 


124 


50 


124 


3 


405 


210 


195 


48 


135 


5 


780 


440 


340 


44 


156 


10 


2980 


2600 


380 


13 


298 


15 


6680 


6610 


70 


1 


445 


30 


10650 


10650 








335 


40 


11670 


11670 








292 



Plotted in Fig. 6. 

these two inductions is a quantity which comes up again and again 
and may be called the ** polarization effect." The polarization effect 
is a measure of completeness of the previous demagnetization. If 
the demagnetization is perfect the polarization effect is zero. The 
first point noted then is that the polarization effect is always positive. 

(2) As the magnetizing force under which the apparent induction 
is measured increases, the polarization effect at first increases, then 
passes through a maximum, and finally decreases to zero. 

(3) The point at which the polarization effect is a maximum is 
somewhat lower than the point of maximum permeability and near 
the point where the differential permeability is a maximum. 

(4) The point at which the polarization effect vanishes is some- 
what above the point of maximum permeability. This vanishing 
point is a critical point magnetically. We shall therefore denote 
the corresponding force and induction as " critical demagnetizing 
force " " and " critical induction.'' 

(5) While the initial polarization effect initially increases, the nor- 
mal induction increases so much faster that the percentage polariza- 
tion effect decreases continuously with increasing magnetizing force. 

To test the nature of this polarization effect still further, the 

" Searle calls this " critical magnetic force.*' 



2l8 



Bulletin of the Bureau of Standards, [yo/. /, No. 2, 



annealed transformer iron was demagnetized and subjected momen- 
tarily to successively increasing polarizing forces. After each appli- 
cation of the polarizing force a magnetizing force of 0.5 was applied 
and slowly reversed several hundred times. After the iron had 
reached a cyclic condition the apparent induction was measured. 




8 



10 11 12 13 14 15 



1 2 3 

H ► 

Tig. 3. — Showing characteristics of annealed transformer iron. 

(Numerical data in Table II.) 

(a) Normal B-H curve. 

(b) Apparent B-H cwive. after intense polarization. 

(c) Polarization effect magnified lo-f old relatively to the -5-//" curves. 

The results are shown numerically in Table VI and graphically in 
Fig. 7. In the curve the apparent induction is plotted against the 
polarizing force. The same figure may be considered as a curve of 
polarization effects, for the distance of the curve below the line of 
normal induction is the polarization effect. It is to be noted that 
the curve of polarization effect plotted against polarizing force 



Burrows.] 



Method of Demagnetizing Iron. 
TABLE VI. 



219 



Showing the influence of various polarizing forces on the apparent 

mduction. 



Polarizing force 


Appftrent induction 


Polarisation effect 


Polarization effect -!- 
polarising force 


.5 


1290 








.6 


1285 


5 


8 


.7 


1260 


30 


43 


.8 


1210 


80 


100 


.9 


1145 


145 


161 


1.0 


1095 


195 


195 


1.5 


925 


365 


243 


2.0 


820 


470 


235 


3.0 


680 


610 


203 


4.0 


605 


685 


171 


5.0 


555 


735 


147 


10.0 


490 


800 


80 


20.0 


480 


810 


40 



Plotted in Fig. 7. 

resembles the ordinary B-H curve with initial slope gradual, then 
passing through a maximum and finally becoming horizontal. 
However, for polarizing forces between zero and the force under 
which the apparent induction is measured, the curve is horizontal. 
This does not mean that polarizing forces less than the magnetizing 
force studied are without any effect on the iron, but that any such 
effect is completely wiped out by the repeated reversals of the 
chosen magnetizing force. 

Certain experiments on the effects of imperfect demagnetization 
seemed to indicate that the data recorded above do not represent the 
maximum possible polarization effects for the given polarizing 
forces. To test this point the polarizing force was applied in dif- 
ferent ways. Experiment showed that a given force left a greater 
residual polarization effect if it were reversed several times than if 
it were simply applied and removed the same number of times. 
The data of Table VII substantiate this conclusion. The last column 
of this table shows the difference in polarization effects under these 



220 Bulletin of the Bureau of Standards, ivoi. 4, No. 2. 

two methods of procedure. It is noticeable that these differences 
are very roughly porportional to the corresponding original polari- 
zation effects. This shows that the change due to the reversals of 
the polarizing force is uniformily distributed, and that the general 
conclusions as to the nature of the polarization effect hold in this 
case as well as in the former. 



14000 


































































^ 




















12000 




















y 


^ 






































/ 


^ 
























1 1000 
















/ 




























9000 














/ 










































f 






























8000 












































7000 

6000 






















































































4A0A 






/ 


^ 




k 




























1 


4nn 








/ 


ii 






\ 


























c 

Q 


300 


^2000 




1 




f 






\ 


{ 
























1 


200 


1000 




/ 


// 


f 








\ 
























C0 


100 




z 




y 












^ 


^^ 























2 3 4 5 6 7 8 9 10 11 12 18 14 15 



Fig. 4. — Showing characteristics of low carbon steel, 
(Numerical data in Table IV.) 

(a) Normal B-H cmire. 

(b) Apparent B-H curve after intense polarization. 

(c) Polarization effect magnified lo-fold relatively to the B-H curves. 

Since the polarization effect is a continuous function of // and 
has a maximum at the same value of //, though of different magni- 
tude in the two methods of polarizing used, it was assumed that the 
polarization effect would be a maximum at the same value of // 
under all conditions, and when it vanished at this force it would 
have vanished for all other magnetizing forces. This is a rather 
bold assumption; but it furnishes a good working basis and econo- 
mizes time, as it allows the characteristics at a single point to typify 



Burrows.] 



Method of Demagnetizing Iron, 



221 



the characteristics of a whole range of points. This assumption is 
later justified for all the ordinary methods of demagnetization. 




10 11 12 13 14 15 



Fig. 5. — Showing characteristics of common sheet iron. 
(Numerical data in Table III.) 

(a) Normal B-H curve. 

(b) Apparent B-// curve after intense polarization. 

(c) Polarization effect magnified lo-fold relatively to the B-H curves. 

UPPER LIMIT OF THE DEHAGNETIZING FORCE. 

It has been assumed in nearly all earlier work " that a necessary 
condition for perfect demagnetization is that the demagnetizing 
current must carry the iron from an induction greater than any 
previous one it has experienced down to a vanishingly small one. 
The question at once arises as to whether a somewhat smaller range 

" See ( I ) on p. 206 and ( i) on p. 207 



222 



Bulletin of the Bureau of Standards, ivou #, No. 2, 



might not be equally successful in wiping out the effects of previous 
polarization. 

To determine the maximum value of a necessary yet sufficient 
demagnetizing force the following experiment was carried out: 
The specimen was first strongly magnetized by a force of 100 to 



































































































11000 
































10000 




























^ 


^ 


9000 






















^ 




^ 


























^ 


^ 




























/ 














6000 
















/ 
















6000 














/ 
















BOO 


4000 








^ 


■^ 


A 


f 
















400 


flOOO 






/ 






t 


















300 


2000 




/ 


f 




A 


\ 


















200 


f 1000 


/ 


/ 




A 


'/ 




\ 
















10Q 


B 


L 




^ 


y 








^ 


















2 4 6 8 10 12 14 16 18 20 22 24 26 28 80 
H ► 

Jig. 6. — Showing characteristics of high carbon steel, 
(Numerical data in Table V.) 

(a) Normal -ff-//" curve. 

(b) Apparent B-// curve after intense polarization. 

(c) Polarization effect magnified lo-fold relatively to the ^-//"curves. 

insure a considerable initial polarization. Then it was demagnet- 
ized from a certain value of the demagnetizing force down to a 
vanishingly small force. The cyclic apparent induction was then 
measured for the value of //", at which the previously observed 



Burrows.] 



Method of Demagnetizing Iron. 



223 



polarization effect was a maximum. After this measurement the 
specimen was again strongly magnetized as before, demagnetized 
from a second maximum down to the same vanishingly small force, 
and finally the cyclic apparent induction was measured for the same 
magnetizing force as before. This process was repeated for a series 




6 7 8 9 
POLARIZING FORCE ► 

Fig. 7. — Showing the relation betiveen the polarizing force and the apparent induction in annealed 

transformer iron for N=0.5. 

(Numerical data in Table VI. ) 

of values of the maximum demagnetizing force. The results of 
these experiments are shown graphically in curves marked " curve 
of upper limits" in Figs. 8, 9, and 10, where the maximum 
demagnetizing forces are plotted as abscissae and the apparent induc- 
tions as ordinates. From these three curves the following charac- 
teristics may be noted : 
11737-07 4 



224 



Bulletin of the Bureau of Standards, [V01.4.N0.2. 



(i) For maximum demagnetizing forces greater than the critical 
demagnetizing force the curve is parallel to the horizontal axis. 
This indicates that the demagnetization is not improved by carrying 
the demagnetizing force beyond this critical demagnetizing force. 

(2) For maximum demagnetizing forces less than the magnetic 
force used to determine the apparent induction the curve is again 
horizontal. This shows that such demagnetization produces no 
effect that the simple reversals of the magnetizing force used in 
determining the induction would not accomplish. 

TABLE VII. 

Showing that the polarizing effect of a field of 100 is greater on reversal 
than on simple make and break. 



force 


Normal Induction 


Polarisation 

effect of make 

and break 


Polarisation 
effect of 
reversals 


Difference 


.3 


370 


240 


290 


50 


.4 


670 


440 


520 


80 


.5 


1290 


810 


910 


100 


.6 


1680 


960 


1080 


120 


.7 


2570 


1190 


1310 


120 


.8 


3370 


860 


1050 


190 


.9 


4300 


600 


730 


130 


1.0 


5130 


380 


500 


120 


1.2 


6730 


240 


330 


90 


1.4 


6950 


90 


110 


20 


1.6 


7610 


30 


30 





2.0 


8880 











3.0 


10750 












(3) The two horizontal portions are connected by a smooth cur\'e, 
indicating that over this range the demagnetization is more or less 
imperfect but is approaching completeness very rapidly with increase 
of maximum demagnetizing force. 

(4) A comparison of the curves for the soft annealed transformer 
iron, the moderately hard low carbon steel, and the hard high carbon 
steel shows that the steepness of this sloping portion of the curve 
and the sharpness of the bends at its upper and lower extremities 
decreases as the hardness of the iron increases. 



BUKPOWi.j 



Method of Demagnetizing Iron. 
TABLE VIII. 



225 



Showing the apparent mduction m annealed transformer iron as influ- 
enced by the upper limit of the demagnetizing force. 



Limits of demag. 
netuins force 


3 (or more)— .a 


a-.a 


X— .a 


.5-.a 




Time interval 


93*4 


73.4 


99 


91.8 


No demaffnet- 
Ixation 


Number of cycles 


M5 


107 


X54 


135 






B 


B 


B 


B 


B 


/r= .3 


370 


360 


320 


11^ 


130 


.4 


670 


670 


630 


360 


230 


.5 


' 1290 


1290 


1210 


740 


480 


.6 


1680 


1680 


1570 


770 


720 


.7 


2570 


2570 


2340 


1530 


1380 


.8 


3370 


3370 


2990 


2460 


2510 


.9 


4300 


4300 


3780 


3580 


3700 


1.0 


5130 


5130 


4620 


4650 


4750 


1.2 


6730 


6730 


6370 


6370 


6490 


1.4 


6950 


6950 


6720 


6710 


6860 


1.6 


7610 


7610 


7390 


7390 


7580 


2.0 


8880 


8880 


8730 


8730 


8880 


3.0 


10750 


10750 


10750 


10750 


10750 



TABLE IX. 
Showing polarization effects (calculated from Table VIII). 



Limits of dexnav- 
nedsins force 


3-.a 


a— .a 


X— .a 


•S-.a 
150 


— % 

No demagnet- 
isation 


.3 





10 


50 


240 


.4 








40 


310 


440 


.5 








80 


550 


810 


.6 








110 


910 


960 


.7 








230 


1040 


1190 


.8 








380 


910 


860 


.9 








520 


720 


600 


1.0 








510 


480 


380 


1.2 








360 


360 


240 


1.4 








230 


240 


90 


1.6 








220 


220 


30 


2.0 








150 


150 





3.0 


1 ^ 















226 



Bulletin of the Bureau of Standards. 
TABLE X. 



\Vol,4.No.2. 



Showing the apparent induction in common sheet iron as influenced by die 
upper limit of the demagnetizing force. 



Limits of demac- 
netlxing force 


lO— I 


7-x 


5-1 




Time interval 


54 


42 


3a 


No demagneti- 
sation 


Number of eyelet 


84 


64 


48 




H 


B 


B 


B 


B 


1 


263 


255 


255 


97 


2 


1314 


1304 


1304 


496 


3 


3770 


3750 


3740 


3130 


5 


7890 


7810 


7700 


7730 


7 


10270 


10200 


10170 


10130 


10 


12170 


12170 


12160 


12160 


15 


13610 


13610 


13610 


13610 



TABLE XL 
Showing polarization effects (calculated from Table X). 



netixing force 


xo— z 


7-x 


5-x 


No demagneti- 
Mtion 


H=\ 





8 


8 


166 


2 





10 


10 


818 


3 





20 


30 


640 


5 





80 


190 


160 


7 





70 


100 


140 


10 








10 


10 


15 















Burrows.} 



Method of Demagnetizing Iron. 
TABLE XII. 



227 



Showing the apparent induction in low carbon steel as influenced by the 
upper limit of the demagnetizing force. 



Limits of demac- 
netisinc force 


x5-.a 


xo— .a 


5-.a 




Time Interval 


70 


70 


49 


No demsfneti- 
xation 


Number of cycles 


xoo 


xoo 


70 






B 


B 


B 


B 


H^ 1 


190 


190 


183 


90 




680 


675 


667 


370 




1930 


1920 


1897 


1460 




4150 


4130 


3990 


3470 




6790 


6745 


6590 


6300 




9140 


9100 


9000 


8670 




9990 


9960 


9920 


9740 




11070 


11060 


11040 


10950 




11880 


11870 


11870 


11820 


10 


12470 


12460 


12470 


12460 


15 


14170 


14170 


14170 


14170 



TABLE Xni. 
Showing polarization effects (calculated from Table XII). 



Limits of demac- 
netising force 


x5-.a 


xo-.a 


5 -.a 


No demacneti- 
Mtlon 










7 


100 







5 


13 


310 







10 


33 


470 







20 


160 


480 







45 


200 


490 







40 


140 


370 







30 


70 


250 







10 


30 


120 







10 


10 


60 


10 





10 





10 


15 















228 



Bulletin of the Bureau of Standards. ivoi. /, no. 2. 



The preceding applies to a single value of the magnetizing force. 
To show that this is typical, and to get further light on the nature 
of the polarization effect under different degrees of completeness in 
the demagnetization, the full range of points was taken for a few 
different sets of magnetizing limits. The data for the apparent 
inductions after various demagnetizations in which the upper limit 



































laoo 












Cu. 


veof 


ipper 


limit 


«? 












1200 
1100 
1000 


1 


/ 




























I 




























































dflO 




\ 




























800 




\ 




























700 






\ 


































\ 


























500 
500 








\ 


N, 








Cu 


veof 


lower 


llmltj 










































400 
flnn 
























































200 

t 100 
B 





























































































1 



10 



11 12 13 14 15 



Fig. 8. — Showing the influence of the upper and lower limits of the demagnetizing 
force on the apparent induction of annealed transformer iron for H=o.^. 

alone was altered are given in Tables VIII, X, and XII. The corre- 
sponding data for the polarization effects are more instructive and are 
given in Tables IX, XI, and XIII. From these six tables the fol- 
lowing conclusions may be drawn: 

(i) The demagnetization is complete throughout the whole range 
if the upper limit is at least as great as the critical demagnetizing 
force. 



Burrows.} 



Method of Demagnetizing Iron, 



229 



(2) If the maximum demagnetizing force is less than the critical 
demagnetizing force, the demagnetization is in general incomplete, 
and the incompleteness extends over practically the whole region 
from the lowest values of the magnetizing force up to the critical 
value. This region may be called the domain of the polarization 
effect. 



8000 


























































—7- 






CurJ 


^eof 


UpD 


jr.Ilr 


Lts 


























— 










































/ 








-- 


Co. 


i:»oi 


'q.Vm 












2fiQO 














/ 








y 








,HHJ 


t& 


lijs^ 






















1 


























^ 
























































/ 




















































































' 






























2700 






























































































, 










































i_ 






























2600 

t 










































JB 











































2 4 6 8 10 12 14 ie 18 20 22 24 26 28 80 82 84 86 88 40 

Fig. 9. — Showing the influence of the upper and lower limits of the demagnetizing 
force on the apparent induction of high carbon steel for H=io, 

(3) The polarization effect increases as the maximum demagnet- 
izing force decreases, but preserves its general characteristics as 
described above. 

(4) In certain cases the polarization effect is greater after a feeble 
demagnetization than without any demagnetization." Tables IX and 
XI for the transformer iron and the common sheet iron, resepctively, 
show this very clearly. This phenomenon occurs at or below the 
point of maximum permeability. It was this peculiar increase of 
polarization that suggested the comparison of polarization effects 

" Cf . Searle's conclusion, 3c on p. 207. 



230 



Bulletin of the Bureau of Standards, 



[Vol. 4, 1^0. », 



after repeated simple make and break, with those after reversals. 
A comparison with those results in Table VII will show that the 
increased polarization effect is still less than the maximum observed 
on reversal. 

Some further observations on the effect of varying the upper limit 
of the demagnetizing force will be made under the discussion of the 
influence of frequency of an alternating current demagnetization on 
the polarization effect. 



700 






















Cur 


/eof 


UPD 


ar llr 


-Jits 
















"^ 


N 






^ 






































\ 


/ 
































$00 










\ 








































/ 


\ 


s. 




































/ 






\ 




































/ 








\ 




























600 






/ 










\ 


s^ 








































V 


\ 


























/ 


















^ 


f^' 


^^fn^ 




















/ 






















s;jcM< 


^ 


^J^^^ 












dttn 




/ 


























"^ 


--- 


..^ 












/ 


































"^ 




1 





















































































2 4 6 8 10 12 14 16 18 20 22 24 26 28 80 82 84 sis 93 ^ 
JBT— * 

Fig. 10. — Showing the influence of the upper and lower limits of the detnagnetizing 
force on the apparent induction of low carbon steel for H=2. 

LOWBR LIMITS OF THE DEMAGNETIZING FORCE. 

Having settled upon a proper value for the upper limit of the 
demagnetizing force, it now remains to determine the necessary and 
sufficient final minimum value of this force. For this purpose an 
experiment similar to the preceding was carried out. The specimen 
was polarized initially as before. The demagnetization was carried 
from a point well above the critical demagnetizing force down to a 
certain minimum value. Finally the cyclic apparent induction was 



Burrows.] 



Method of Demagnetizing Iron. 



231 



measured for the ^lame force as in the preceding experiment. These 
operations were repeated, modifying only the final minimum value 
of the demagnetizing force. The results of this experiment are 
shown graphically in the curves marked " curve of lower limits " in 
Figs. 8, 9, and 10. The minimum value of the demagnetizing 
force is plotted as abscissa and the corresponding cyclic apparent 
induction as ordinate. Both coordinates are plotted to the same 
scale as in the curve of upper limits. From these curves the fol- 
lowing conclusions may be drawn: 

TABLE XIV. 

Showing the apparent induction of annealed transformer iron as influenced 
by the lower limit of the demagnetizing force. 



Limits of demag- 
netislnK force 


x5-.3a 


X5-.5 


X5-I.X5 


x5-«.6 




Time interval 


95.8 


97.8 


66 


60 


No demagnet- 
ixatlon 


Number of cycles 


x6o 


X55 


X04 


96 




H 


B 


B 


B 


B 


B 


.3 


370 


352 


250 


160 


130 


.4 


670 


660 


450 


340 


230 


.5 


1290 


1290 


990 


645 


480 


.6 


1680 


1680 


1470 


1000 


720 


.7 


2570 


2570 


2420 


1800 


1380 


.8 


3370 


3370 


3180 


2700 


2510 


.9 


4300 


4300 


4270 


3870 


3700 


1.0 


5130 


5130 


5110 


5030 


4750 


1.2 


6730 


6730 


6730 


6690 


6490 


1.4 


6950 


6950 


6950 


6950 


6860 


1.6 


7610 


7610 


7610 


7610 


7580 


2.0 


8880 


8880 


8880 


8880 


8880 


3.0 


10750 


10750 


10750 


10750 


10750 



(i) For values of lower limit of the demagnetizing force less than 
the magnetizing force which produces the apparent induction, the 
curve is a horizontal line. This indicates that the demagnetization 
is not improved by carrying the demagnetizing force below the 
lowest magnetizing force to be studied. 



232 



Bulletin of the Bureau of Standards. \voi. <. no.*. 



(2) For values of the lower limit considerably greater than the 
critical demagnetizing force the curve is a horizontal straight line 
and indicates that the demagnetizing force does not modify the 
previously existing polarization efFect ; at least it does not modify 
that portion of it which repeated reversals of the given magnetizing 
force do not eliminate. 

(3) Between the two horizontal portions is a continuous sloping 
curve, which indicates a partial demagnetization which increases in 
completeness very rapidly as the lower limit of the demagnetizing 
force decreases. 



TABLE XV. 

Showing the apparent induction of common sheet iron as influenced by 

the lower limit of the demagnetizing force. 



UmlUofdemag- 
netUlng force 


X5-X 


15-a 


X5-3 


X5-5 


X5-7 




Time interval 


38 


37 


31 


23 


17 


No demag- 
netisation 


Number of eyelet 


56 


5a 


48 


3a 


a6 




H 


B 


B 


B 


B 


B 


B 


1 


263 


255 


197 


151 


120 


97 


2 


1314 


1314 


1224 


890 


820 


496 


3 


3770 


3770 


3770 


3350 


3220 


3130 


5 


7890 


7890 


7890 


7890 


7860 


7730 


7 


10270 


10270 


10270 


10270 


10270 


10130 


10 


12170 


12170 


12170 


12170 


12170 


12160 


15 


13610 


13610 


13610 


13610 


13610 


13610 



(4) A comparison of the curves for three grades of iron and steel 
shows that the steepness of the curved portion and the sharpness of 
the bends at the upper and lower extremities decrease as we pass 
from the softer to the harder material. The lower horizontal por- 
tion occurs at extremely high values in the hard material. (Figs. 
9 and 10.) 

To justify the above conclusions drawn from measurements made 
at a single value of the magnetizing force, and to investigate further 
the nature of the polarization efFect several complete apparent induc- 
tion curves were obtained under difFerent details of demagnetization. 



Burrows.] 



Method of Demagnetizing Iron, 



233 



These complete data are given in Tables XIV, XV, and XVI. From 
these data the preceding conclusions are justified, and the following 
generalization appears: If the demagnetization is carried from the 
critical demagnetizing force down to a certain pointy the demagnet- 
ization is complete for all values above the final demagnetizing force. 
For magnetizing forces below this final value of demagnetization the 
demagnetization is incomplete^ and the incompleteness is greater the 
greater the interval between the final demagnetizing force and 
the magnetizing force used to produce the induction desired, 

TABLE XVI. 

Showing the apparent induction of low carbon steel as influenced by the 
lower limit of the demagnetizing force. 



Limits of demag- 
netising force 


i5-.a 


x5-a.5 


X5-3 


X5-5 




Time interval 


75 


73 


167 


"• 


No demagnet- 
Ixation 


Number of cyclea 


83 


80 


900 


z8o 




H 


B 


B 


B 


B 


B 




190 


185 


175 


152 


90 




680 


680 


668 


566 


370 




1930 


1930 


1930 


1795 


1460 




4150 


4150 


4150 


4150 


3470 




6790 


6790 


6790 


6790 


6300 




9140 


9140 


9140 


9140 


8670 




9990 


9990 


9990 


9990 


9740 




11070 


11070 


11070 


11070 


10950 




11880 


11880 


11880 


11880 


11820 




12470 


12470 


12470 


12470 


12460 




14170 


14170 


14170 


14170 


14170 



EDDY CUSRSNTS— THEORY. 

If we use an alternating current in demagnetizing, we must 
consider the shielding effect which the eddy currents exert on the 
interior of the specimen. The magnetizing force at any point is the 
resultant of the force due to the current in the wire and the force 
due to the eddy currents in the specimen. The calculation of this 



234 Bulletin of the Bureau of Standards. ivoi. 4. No. 2. 

force presents great difficulties unless certain simplifjHing assump- 
tions are made. Heaviside^^ in a paper entitled " The Induction of 
Currents in Cores," gives a solution for the special case of a round 
rod of constant permeability magnetized by a simple harmonic force. 
In this case the force at any point of the specimen is a function of 

/i=the permeability. 

/»=the specific resistance. 
N= the frequency. 

r=the distance of the point from the axis. 

If we let x= — ^— - the resultant magnetic force at any point is 

I/=AM+BN, 
where A and B are constants, and 



2 






XT' :x^r* . ;rV 



~ 2» 2!4»6'^2'4-6^8!io' 

The maximum value of H at any point in the core is proportional to 



By squaring the expressions for M and N^ and adding, we have 



-^ + 2VV + 6^8*V^ + io!i2*V +H^^i8?2o'V +••■ 

where y=x'r*. 

Since every term of the series is positive, the amplitude increases 
as we pass from the axis outward. To get some idea of the relative 

" Electrical Papers, Vol. I, p. 353 ft. 



Bmrrtws.] Method of Demagnetizing Iron. 235 

magnitude of the amplitudes at various distances from the axis, 
I have calculated values of ^M^+JST for different values of y. 
These calculated values are shown graphically in Fig. 25, where 
^M^+JS^ is plotted as abscissa and y as ordinate. ^M^+JS^ is 
the ratio of the amplitude for a given value of y to the amplitude 
at the center where y is zero. 
Putting 

fi=1000 

/»= loooo c. g. s. units (=10 micro-ohms) 
^=60 



we have 



j)/=;r»r* 



^=224000 r^ 

The last equation is plotted on the left half of Fig. 25 in connec- 
tion with the curve of amplitudes; y is plotted upward on the same 
axis for both curves. The distance from the center r is plotted to 
the left. Curves are drawn also for fi=^oo and fi= 2000. From 
this figure the relative amplitudes at any distance from the axis 
may be obtained, subject of course to the conditions stated above. 
Apply this to a rod of the dimensions of the low carbon rod already 
used. If /i=500, a point on the surface, r=o.29 ^™) corresponds 
to the point P on the (^, r) curve and Q on the (-^Af^+N^y y) 
curve, so that at the surface of the rod the maximum induction is 
4.4 times its value at the axis. For /a =1000 the maximum induc- 
tion at the boundary is 14 times the value at the axis. The induc- 
tion has half the boundary value at r= 0.235 cm, showing that the 
resultant force, and consequently the induction, is much greater in 
the outer layers of the rod. The flatness of the (^, r) curve for 
small values of r shows that the force and flux are nearly uniform 
near the axis of the rod. This variation of the resultant magnetic 
force throughout the cross section of the rod increases with increase 



226 



Bulletin of the Bureau of Standards. 
TABLE X. 



\yol.4.NQ.2, 



Showing the apparent induction in common sheet iron as influenced by the 
upper limit of the demagnetizing force. 



LimltB of demac- 
netixing force 


lO-X 


7-x 


5-x 




Time Interval 


54 


4a 


39 


No demegneti- 
xation 


Number of cycles 


84 


64 


48 




H 

1 
2 
3 
5 
7 
10 
15 


B 

263 

1314 

3770 

7890 

10270 

12170 

13610 


B 

255 

1304 

3750 

7810 

10200 

12170 

13610 


B 

255 
1304 
3740 
7700 
10170 
12160 
13610 


B 

97 

496 

3130 

7730 

10130 

12160 

13610 



TABLE XI. 
Showing polarization effects (calculated from Table X). 



Limite of demaff- 
netixlng force 


XO— X 


7-x 


5-x 


No demagneti- 
sation 


H=l 





8 


8 


166 


2 





10 


10 


818 


3 





20 


30 


640 


5 





80 


190 


160 


7 





70 


100 


140 


10 








10 


10 


15 















Method of Demagnetizing Iron. 
TABLE XII. 



227 



Showing the apparent induction m low carbon steel as influenced by the 
upper limit of the demagnetizing force. 



Limita of demac- 
netlslox force 


x5-.a 


xo-.a 


5-.a 




Time Interval 


70 


70 


49 


No demairnetl- 
xatlon 


Number of cycles 


zoo 


zoo 


70 






B 


B 


B 


B 


H^ 1 


190 


190 


183 


90 




680 


675 


667 


370 




1930 


1920 


1897 


1460 




4150 


4130 


3990 


3470 




6790 


6745 


6590 


6300 




9140 


9100 


9000 


8670 




9990 


9960 


9920 


9740 




11070 


11060 


11040 


10950 




11880 


11870 


11870 


11820 


10 


12470 


12460 


12470 


12460 


15 


14170 


14170 


14170 


14170 



TABLE Xra. 
Shovni^ polarization effects (calculated from Table XII). 



Limits of demaff- 
netisins force 


z5-.a 


zo— .a 


5 -.a 


No demagneti- 
xation 










7 


100 







5 


13 


310 







10 


33 


470 







20 


160 


480 







45 


200 


490 







40 


140 


370 







30 


70 


250 







10 


30 


120 







10 


10 


60 


10 





10 





10 


15 















238 



Bulletin of the Bureau of Standards. 



\yol.4,NQ,t, 



and with the massive yokes, respectively. Graphic representations 
of the data for the low and the high carbon steels are given in 
Figs. 1 2 and 1 3. Table XVII gives a portion of the numerical data for 
all three of the specimens in a form which facilitates comparison. 
From the graphic and numerical data given above a number of con- 
clusions may be drawn. 

































































LiJ 


e 


bf( 


or 


I^Pl 


^ 


d 


>nn 


M 


ie 


izfl 


tlOj 


T 














700 


























































^ 






















































*** 





































600 
















































— 






















































































































































500 






































































































































































































400 


























































Lh 


te 


)f 


\o 


je 


na 


an 


9tl 


^ 


or 
































1 












































































































































800 








































































































































































































£00 






















































































































































100 


































































































t 
7? 





















































































































































25 



50 76 

NUMBER OF CYCLES PER SECOND 



100 



Fig. 12. — Showing the influence of the demagnetizing frequency on the apparent 
induction of low carbon steel for H=2. 

(i) In every case an increase in the frequency of the demagnetiz- 
ing current is accompanied by a decrease in the apparent induction 
as subsequently measured. 

(2) In the case of the transformer iron, the polarization effect 
which is measured by the distance of the curve below the upper 
horizontal line is greater as the cross section of the yokes increases. 
That the polarization effect does not vanish when the yokes are 



Burrows.] 



Method of Demagnetizing Iron, 



239 



removed shows that while the yokes modify its magnitude, they 
are not the cause of it. In comparing the transformer iron with the 
other specimens the data obtained with the massive yokes should 
be used, as heavy yokes were used on the other specimens. 























































800 


































































Llr 


eo 


cor' 


2pU 


rte 


aerr 


a£ 


letl 


ati 


?n 






























■""■ 






























































































700 














































































































































































































600 
















































































































































































































AOO 






















































































































Lir 


eo 


no 


der 


nag 


net 


izat 


on 






























































































































400 
















































































































































































































800 
















































































































































































































200 














































































































































































































100 






































































































t 

























































































































































25 



60 76 

NUMBER OF CYCLES PER SECOND 



100 



126 



Fig. 13. — Showing the injluence of the demagnetizing frequency on the apparent 
induction of high carbon steel for H—$. 
11737-07 ^5 



240 



Bulletin of the Bureau of Standards, \vol 4, so, 7. 



(3) The diminution in apparent induction — that is, the polariza- 
tion effect — is relatively greater in the softer material. This state- 
ment holds also for the maximum polarization effect, as measured by 
the distance between the line of perfect demagnetization and the line 
of no demagnetization. The rate of increase of the polarization 
effect with the frequency of the demagnetizing current is greater 
in the softer materials. 

TABLE XVIII. 



Showing the nature of the polarization effect remaining in annealed trans- 
former iron after demagnetizing by alternating current of 60 cycles. 





♦5-.2 


3.5-2 


a.6-.a 




Time interval 


77 


58 


34 


No demagneti- 
sation 


Number of cycles 


4fao 


34«o 


acHo 




K 


Normal 
induction 




PolariMtion effects 




.3 


370 


20 


30 


30 


240 


.4 


670 


30 


30 


40 


440 


.5 


1290 


50 


50 


70 


810 


.6 


1680 


60 


60 


90 


960 


.7 


2570 


80 


80 


100 


1190 


.8 


3370 


70 


70 


70 


860 


.9 


4300 


60 


60 


60 


600 


1.0 


5130 


50 


50 


50 


380 


1.2 


6730 


40 


40 


40 


240 


1.4 


6950 


20 


20 


20 


90 


1.6 


7610 


10 


10 


10 


30 


2.0 


8880 












♦This column holds also for the following conditions: 






Limits of demagnet- 
ising force 


5-a 


ao— .a 




36-.a 


i59--a 


Time interval 


X77 


40.8 


- - 


60 


5a 


Number of cycles 


4690 


3448 


3600 


3xao 



Burrows.] 



Method of Demagnetizing Iron. 



241 



NATURE OF POLARIZATION DUE TO FREQUENCY. 

That the above conclusions, based on a single value of the mag- 
netizing force, hold in general is clear from data obtained to show 
the nature of the polarization effect throughout the whole range of 
the induction curve. Table XVIII shows such a set of data for the 
annealed transformer iron where the results are expressed in terms 
of polarization effects. Several things in this table are worthy of 
note. 

TABLE XIX. 

Showing the nature of the polarization effect remaining in low carbon steel 
after demagnetizing by an alternating current of 60 cycles per second. 



Limits of demagnetixing force 


90.x— .a 


4a.4-.3 


x6.3— .a 




Time interval 


xaa.8 


X40.6 


xx8 


No demagneti- 
sation 


Number of cycles 


7368 


6436 


7080 




// 


Normal 
induction 




Polarization effects 






190 





12 


16 


100 




680 


20 


50 


85 


310 




1930 


45 


120 


200 


470 




4150 


100 


280 


420 


480 




6790 


70 


280 


300 


490 




9140 


70 


200 


210 


370 




9990 


60 


110 


140 


250 




11070 


50 


60 


90 


120 




11680 


20 


20 


20 


60 


10 


12470 











10 



Plotted in Pig. 14. 

(i) The polarization effect exists for all values of the magnetiz- 
ing force up to the critical demagnetizing force, but is much smaller 
than the maximum polarization effect observed after intense mag- 
netization without subsequent demagnetization. In this respect it 
resembles the effect after the imperfect demagnetization due to the 
upper limit of the demagnetizing force being too low. 

(2) The polarization effect is constant for all values of the initial 
demagnetizing force greater than 5. A reference to Table VIII will 



243 



Bulletin of the Bureau of Standards. [yoi. /, no. 2. 



show that for slow frequency the maximum demagnetizing force of 
2.0 or over gave constant results. An alternating current then 
requires a greater initial maximum to produce its full effect 

(3) The polarization effect after a demagnetization by alternating 
current, even when this has a value great enough to produce its 
maximum effect, is of considerable magnitude and extends from the 
smallest values of the magnetizing force up to the critical demag- 
netizing force. 































1 






















































H-4 


\ 






























400 










\ 








































\ 
































H^ 








X 


N, 
































...v^ 


=X 


>^ 




































X: 


^ 


X, 




















H-6 


__ 
















s.^^V 


^ 












2U0 


1 




H=3 


\ 


X 










^^ 


^ 


^ 


X 


^ 


^. 










c 



























■\ 




N 








-| 




H-7 


_^_ 








'^ 




^^ 










V 




^ 


^ 


100 


— * 




H-2 


-- 


..^ 














■"^ 




^ 


■^ 


-^ 


^v. 


^ 


















—- 




— 















■"^ 


-- 








H-1 


.... 






















' 














1 





2 





Z 


10 


4 





6 





G 





j 





8 





90 



MAXIMUM DEMAGNETIZING FORCE 

Jig. 14. — Showing how the polarization effect in low carbon steel due to excessive 
frequency varies with the maximum demagnetizing force, 

(Numerical data in Table XIX.) 

The low carbon steel was examined in the same way. The data 
for this have been shown numerically in Table XIX and graphically 
in Fig. 14. For this specimen also the polarization exists for all 
values of the magnetizing force up to the critical value. A constant 
value, however, was not reached at the values of the maximum 
demagnetizing forces used, even though a value over six times the 
maximum required at low frequency was used. 



Burrows.l 



Method of Demagnetizing Iron, 



243 



THE CAUSE— EDDT CURRENTS. 

As was expected, the demagnetizing eflBciency of an alternating 
current is less than that of a slowly reversed direct current. This 
diflEerence is much greater in the thick round rod of low carbon 
steel than in the thin strip of transformer iron. (See dimensions in 
Table I.) Referring to Fig. 25 and assuming a mean permeability 
of 1 000 for the round rod we see that the magnetic force on the axis 
is only 7 per cent of the magnetizing force exerted by the alternating 
current of 60 cycles. The alternating current furnished a magnet- 

TABLE XX. 

Showing the influence of eddy currents during the demagnetization by 
alternating current on the residual polarization effect. 



Limits of demmgnetixing 
force 



Time intervml 



Frequency 



Normal 
induction 



.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

1.2 

1.4 

1.6 

2.0 



370 
670 
1290 
1680 
2570 
3370 
4300 
5130 
6730 
6950 
7610 
8880 



X5- 



1-7 



5.3- 



57.a 



60 



17.6 --.a 



a8— .a 



69.8 



60 



155-.3 



65.6 



53.8 



Polarization effects 



20 

40 

90 

110 

170 

210 

220 

240 

200 

150 

80 

30 



70 


30 


30 


20 


130 


70 


50 


50 


250 


120 


100 


100 


400 


180 


160 


120 


620 


290 


250 


230 


720 


320 


280 


250 


740 


340 


300 


260 


660 


350 


280 


240 


480 


320 


250 


240 


350 


290 


200 


190 


320 


250 


180 


160 


240 


180 


100 


100 



40 
90 
170 
280 
400 
460 
480 
500 
420 
320 
300 
200 



Plotted in Fig. 15. 

izing force of 30 units, so that in the case of the low carbon steel 
where the induction does not reach a constant value at the magnet- 
izing forces used, the incompleteness is due to the combined effect 
of frequency and too low magnetizing current. In the case of the 



244 



Bulletin of the Bureau of Standards, 



[rol. 4, JVo. ^. 



annealed iron, however, increased current does not reduce the polar- 
ization effect to zero, so that here we have an effect due solely to the 
frequency. 

There seems no doubt that this decrease in induction after demag- 
netizing by alternating current is mainly an eddy current effect ; 




10 20 

MAXIMUM DEMAGNETIZING FORCE 

Fig. 15. — Shozving how the polarization effect in a specimen of annealed trans- 
former iron surrounded by a copper tube^ after demagnetization by an 
alternating current ofdo cycles ^ varies with the maximum demagnetize 
ing force. 

(Numerical data in Table XX.) 

nevertheless, to test this point further, one of the strips of annealed 
transformer iron was placed in a copper tube and the inductions 
measured in the regular way after various demagnetizations. The 



Borrows.] Mcthod of Demagnetizing Iron. 245 

data have been expressed as polarization effects and are recorded 
numerically in Table XX and graphically in Fig. 15. From the 
table we may draw a number of conclusions. 

(i) The polarization effect even after slow reversals is not zero as 
we should expect it to be for perfect demagnetization. 

(2) The polarization after a maximum demagnetizing force of 5 is 
much greater than it was when the copper tube was. off. As the 
maximum force increases the polarization effect decreases through- 
out the whole range of magnetizing forces in much the same way 
as it does when the polarization effect is decreased by carrying the 
upper limit of a slowly reversed demagnetizing force up nearer and 
nearer to the critical value. The sixth and eighth columns of this 
table show that doubling the demagnetizing frequency, other con- 
ditions remaining unaltered, approximately doubles the polarization 
effect 

(3) The curves of Figs. 14 and 15 were drawn primarily to 
show how the polarization effect decreases as the upper limit of the 
demagnetizing force increases. The form of these ciurves is inter- 
esting. For the lower values of -^ these curves are concave upward. 
As the value of H increases the initial curvature increases, reaches 
a maximum in the neighborhood of the maximum of the perme- 
ability, finally decreases and becomes convex upward for the higher 
values of H. Other data seem to indicate that all of these curves 
become concave upward for large values of the upper limit of the 
demagnetizing force. 

CONSTAIVCY OF RESULTS. 

Another and very important fact brought out during the course 
of these experiments is the uniform consistency with which results 
are reproduced. Thus, while an alternating current of a frequency 
of 90 cycles per second will give a residual polarization effect it 
always gives the same residual value, and the induction curve 
obtained after such demagnetization may be repeated any number 
of times. No evidence of imperfect demagnetization exists except 
the fact that higher inductions may be obtained under other methods 
of demagnetization. This probably accounts for the fact that so 
many experimenters consider an alternating current demagnetization 
as entirely satisfactory. Furthermore, the polarization effect remain- 



■^'"o;' 






246 



Bulletin of the Bureau of Standards. \ voi. /, No. 3. 



ing after demagnetization by alternating current decreases with 
decrease in the thickness of the specimen so that in the case of the 
thin transformer iron, such as that used in this investigation 
(.036 cm), or in the work of Professor Searle (.034 cm and .037 
cm), the error introduced by imperfect demagnetization is negli- 
gible except in the steep part of the B-H curve. It is in the case 
of specimens of large cross section that the objections to alternating 
current demagnetization have most weight. 

TABLE XXI. 

Showing the nature of the residual polarization effect in annealed trans- 
former iron caused by the time interval of demagnetization being too 
brief. 



Limits of demagnetlxing force 


15 -.a 


x5-.a 


x5-.a 




Time interval 


74 or over 


58 


30 


No demagnet- 
ization 


Number of cycles 


no or over 


85 


VJ 




H 


Normal 
induction 


Polarisation effects 


.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

1.2 

1.4 

1.6 

2.0 


370 
670 
1290 
1680 
2570 
3370 
4300 
5130 
6730 
6950 
7610 
8880 
















10 

20 

20 

30 

50 

40 

40 

20 










30 

70 

80 

100 

150 

120 

110 

60 

40 








240 

440 

810 

960 

1190 

860 

600 

380 

240 

90 

30 





As a general conclusion from the preceding, it is evident that the 
best demagnetization is obtained with the slowest reversals. As, 
however, the curves of Figs. 11, 12, and 13 cut the vertical axis at 
a value of the induction not far different from the value at a demag- 
netizing frequency of one cycle per second, we may without sensi- 



Burrows. J 



Method of De^nagnetizing Iron. 



247 



ble difference and with great economy of time use a frequency of 
one cycle per second in practice. The fact that the constant value 
of the apparent induction after the best demagnetization which a 
6ocycle current can give is less than the normal induction indicates 
that something else besides eddy currents is reducing the value of 
the induction. This something is probably closely related to the 
phenomenon of magnetic viscosity. 

TIME mXERVAL OF DEMAGNETIZATION. 

Having determined the proper frequency and limits for the demag- 
netizing force it now remains to determine the effect of variations in 
the time interval of demagnetization. With this in view the iron 



TABLE XXII. 

Showing the nature of the residual polarization effect in common sheet iron 
caused by the time interval of demagnetization being too brief. 



Limits of demmgDetixlng force 


i5-.a 


X5-.2 


x5-.a 


15. -a 




Time interval 


58.3 or over 


33.6 


x8 


7 


No demag- 
netization 


Number of cycles 


8a or over 


53 


as 


XX 




H 


Norma! 
induction 




Pola 


rixation effec 


\M 




1 


263 





15 


18 


28 


166 


2 


1314 





26 


94 


124 


818 


3 


3770 





50 


105 


130 


640 


5 


7890 





25 


35 


60 


160 


7 


10270 








10 


20 


140 


10 


12170 














10 


15 


13160 


















was demagnetized at a slow rate of reversal and between the demag- 
netizing limits determined upon above. This was done a number 
of times, varying the time interval of demagnetization ; that is, the 
number of cycles. The numerical results for transformer iron, com- 
mon sheet iron, and low carbon steel are given in Tables XXI, XXII, 
and XXIII. From these data it appears that the polarization effect 



248 



Bulletin of the Bureau of Standards. 



[fol. /. -Vo. 2, 



is zero for all values of the magnetizing force, provided the demag- 
netization has taken approximately a minute. If the time is too brief 
the polarization effect extends over nearly the whole range from the 
lowest values up to that of the critical demagnetizing force. It 
increases in magnitude as the time decreases. Too brief a time 
interval has the same effect as too small a current or too high a 

TABLE XXIII. 

Showing the nature of the residual polarization effect in low carbon steel 
caused by the time interval of demagnetization being too brief. 



Limits of demagnetising force 


15 --a 


x5-.a 




Time interval 


75 or over 


67 


No demagneti- 
sation 


■ 
Number of cycles 


83 or over 


xoo 




// 


Normal induction 


Polarisation effects 


1 


190 








100 


2 


680 





5 


310 


3 


1930 





20 


470 


4 


4150 





25 


480 


5 


6790 





40 


490 


6 


9140 





25 


370 


7 


9990 





20 


250 


8 


11070 








120 


9 


11880 








60 


10 


12470 


<» 





10 


15 


14170 












frequency. A comparison of the polarization effect after no demag- 
netization with that after the briefest interv^al shows that the greater 
portion of the polarization effect is wiped out by the first few 
reversals. 

Table XXIV shows the effects of variations in the time interval 
when the demagnetization is carried on at a somewhat higher fre- 
quency. The full effect of the demagnetization while less than 
before is reached in a shorter interval of time and therefore seems to 
depend on the number of cycles rather than the time. From this it is 



Burrows.] 



Method of Demagnetizing Iron. 
TABLE XXIV. 



249 



Showing how the time interval of demagnetization influences the apparent 

induction. 



Demmgnetlxing frequency =14 



Time interval 



Number of cycles 



Apparent induction 



Annealed transformer iron for H=.^ 



No demagnetizatioii 



10 

14 

25 

26 

47 

130 

273 

310 



140 

196 

350 

364 

658 

1352 

3822 

4340 



Normal 



480 
1225 
1240 
1265 
1265 
1265 
1265 
1265 
1265 
1290 



Low carbon eteel for H=% 



No demagnetization 



2.4 
3.2 
4.2 

4.6 

7.4 

18.0 

44.0 



34 

45 

59 

64 

104 

252 

616 



Normal 



370 
640 
649 
660 
661 
662 
662 
662 
680 



High carbon steel for H=io 





No demagnetization 




2600 


26 






364 


2960 


53 






742 


2960 


126 






1764 


2960 


221 






3094 


2960 




Normal 




2980 



250 



Bulletin of the Bureau of Standards, ivoi. /, No. a. 



evident that if the time of demagnetization is kept constant while 
the frequency is varied, there will be a tendency for the induction 
to increase as the frequency decreases as long as the time interval 
is great enough to allow the demagnetizing current to accomplish 





























1400 


























1200 
1100 
1000 


^ 


^ 
















-_«^_ 


_ 






/ 
























/ 
























/ 
























aoo 

700 
600 










































































600 


























4QO 




















































200 


























100 




















































FREC 


5 1 
lUENO 


1 

( 


6 2 


2 


5 3 


a 


6 4 


4 


o & 


. 6 


5 60 



Fig. 16. — ShoTving the combined effect of frequency and time interval of demagneti- 
zation on the apparent induction of transformer iron when H=o.^. 

its full effect. For the lower frequencies, though a greater efficiency 
is possible, a longer time is required, and if this is too short the 
effect of the briefness may exceed the advantage due to the slower 
frequency and the induction diminishes from a certain point on as 



Snrrows.] 



Method of Demagnetizing Iron. 



351 



the frequency decreases. This is exactly what happened in one of 
the earlier experiments of this investigation. A portion of the 
data obtained is shown graphically in Fig. 16. This curve led 
to the erroneous conclusion that a frequency of fourteen cycles per 
second w^as the best frequency for the demagnetizing current. 

THE NORMAL INDUCTION. 

After the iron has been thus freed from all traces of previous 
magnetic polarization it is ready for the ballistic determination. 



A&nn 












































\ 










































\ 


V 










































\ 






































NOUO 




\ 


v 
































• 








\ 




































Z 








\ 


































Id 










\ 


V 






























flC 

^3700 












s 


\ 


























































































\ 


^ . 














































^ 


. 












SfiBO 


































* 


— 





































































































10 











2C 


K) 








8C 


K) 








400 



NUMBER OF CYCLE 

Fig. 17. — Shoimng the fnanner in which the apparent induction of an iron ring 
changes on successive reversals of the magnetizing force. 

We have earlier defined true induction as the normal cyclic induc- 
tion. The reason for this is apparent from the following: 

The induction at the point of maximum differential permeability 
in a bundle of ring stampings of thin annealed transformer iron was 
determined for successive reversals of the magnetizing force. The 
results appear in Fig. 17, where the number of the cycle is plotted 
on the horizontal axis and inductions along the vertical. The ver- 



252 



Bulletin of the Bureau of Standards, 



[ Vol. /, No, 2. 



tical scale is greatiy enlarged so as to show the characteristics of the 
curve. This curve shows three characteristic parts. The first 
few reversals show a rapidly increasing apparent induction, then a 
maximum value is passed, and finally the apparent induction 
decreases, at first quite rapidly, then more and more gradually, and 
finally approaches a lower limit asymptotically. As the test speci- 
men in this case is an endless ring with the magnetizing coil wound 













































4400 


A 












• 






























\ 












































V 










































\ 












































\ 




































4300 






\ 


V 










































^ 


s. 










































^ 


"^ 


















































■ — 








































D 


"^^ 


■-- 




-— 
















t 

B 






























— - 


== 




^ 












































4100 





















































































60 



100 
NUMBER OF CYCLE 



160 



Rg. 18. — Showing the manner in which the apparent induction of low carbon steel 

changes ivith successive reversals oftheforc^ H=4. 

(a) with yokes, and (b) without yokes. 

uniformly this phenomenon can not be due to any end effect. 
Similar curves taken with straight rods of low carbon steel are 
shown in Fig. i8. The curve "a" represents data in which the 
rods were joined together by yokes, while for curve " b " the rods 
were not joined but placed as close as the magnetizing coils would 
allow. These two curves have the same characteristics as the one 
obtained from the ring. They are so nearly alike that no modify- 
ing effect can be attributed to the yokes. To examine more fully 
the manner in which the cyclic state is reached for various values 



Burrows.] 



Method of Demagnetizing Iron, 



253 



of the magnetizing force, complete induction curves were obtained 
foi several values of the magnetizing force after certain numbers of 
reversals. This was done for annealed transformer iron, low carbon 
steel, and high carbon steel, and the data are given in Tables XXV, 
XXVI, and XXVII, and in part are shown graphically in figures 19, 
20, and 21. Both from the curves and the summaries at the bottom 

TABLE XXV. 

Showing the manner in which completely demagnetized transformer iron 
approaches the cyclic state. 



Number of cycle 






Apparent induction 






















^=.5 


5350 


/r=a 


^=3 


^=5 


H=io 


y/-i5 


1 


1300 


9100 


10850 


12800 


14620 


15280 


2 


1325 


5400 


9200 


11000 


12810 


14630 


15290 


3 


1320 


5440 


9210 


11020 


12800 


14630 


15280 


4 


1320 


5470 


9200 


11020 


12780 


14630 


15280 


5 


1320 


5490 


9190 


11010 


12770 


14620 


15280 


20 


1318 


5400 


9100 


10950 


12750 


14620 


15280 


50 


1310 


5300 


9030 


10880 


12750 


14620 


15280 


100 


1302 


5215 


8970 


10810 


12750 


14620 


15280 


200 


1294 


5150 


8915 


10760 


12750 


14620 


15280 


400 


1292 


5140 


8890 


10760 


12750 


14620 


15280 


600 


1290 
1325 


5130 


8880 


10750 


12750 


14620 


15280 


^^ 


5490 


9210 


11020 


12810 


14630 


15290 


^f^XMl 


1290 


5130 


8880 


10750 


12750 


14620 


15280 


^■« — ^nii»i 


35 


360 


330 


270 


60 


10 


10 


■^flaal 


.03 


.07 


.04 


.03 


.00 


.00 


.00 



Plotted in Fig. 19. 

of the tabulated data it is evident that the difference between the 
maximum apparent induction and its final value increases in all the 
specimens as the value of //'used approaches that of maximum per- 
meability. This difference in apparent inductions divided by the 
final apparent induction gives a quotient which is a maximum at 
approximately the point where the differential permeability is a 



254 



Bulletin of the Bureau of Standards. \voi. 4, No. i. 



maximum. No marked difference in the manner in which the vari- 
ous specimens approach the cyclic state can be noticed. Any irregu- 
larities that occur in the curve indicating the manner of approach 
are found during the first few cycles, and are due probably to a 

TABLE XXVI. 

Showing the manner in which low carbon steel approaches the cyclic state 
after one initial demagnetization. 



Number of cycle 






Apparent Induction 






















//-I 


^-3 


//=4. 


^=5 


y/=7 


//-xo 


^-X5 


1 


191 


1920 


4210 


6860 


10060 


12450 


14170 


2 


192 


1930 


4240 


6890 


10070 


12510 


14180 


3 


192 


1940 


4270 


6920 


10070 


12500 


14180 


4 


192 


1960 


4280 


6920 


10060 


12500 


14180 


5 


192 


1970 


4290 


6925 


10060 


12490 


14180 


6 


191 


1980 


4290 


6930 


10060 


12490 


14170 


7 


191 


1990 


4290 


6930 


10050 


12490 


14170 


8 


190 


1990 


4290 


6930 


10050 


12480 


14170 


9 


190 


1985 


4280 


6930 


10050 


12480 


14170 


10 


190 


1985 


4280 


6925 


10050 


12470 


14170 


20 


190 


1980 


4260 


6905 


10040 


12470 


14170 


50 


190 


1970 


4250 


6880 


10030 


12470 


14170 


100 


190 


1960 


4220 


6850 


10020 


12470 


14170 


200 


190 


1950 


4190 


6810 


10010 


12470 


14170 


400 


190 


1940 


4160 


6800 


9990 


12470 


14170 


600 


190 


1930 
1990 


4150 


6790 


9990 


12470 


14170 


B^ 


192 


4290 


6930 


10070 


12510 


14180 




190 
2 


1930 
60 


4150 
140 


6790 
140 


9990 
80 


12470 
40 


14170 


^max — ^rin.l 


10 




.01 


.03 


.03 


.02 


.01 


.00 


.00 



Plotted in Fig. 20. 

small residual polarization which is large enough to modify the first 
reversal but is soon wiped out by continued reversals. Such irregu- 
larities might be expected in accordance with the theory of molecular 
magnets. In view of the preceding experiments it seems quite proper 



BurKnifs.] 



Method of Detnagnetizmg Iron. 



255 



to fix upon the final minimum value of the apparent induction as 
the definition of the true normal induction. The initial and maxi- 
mum values are rejected because of their uncertainty and the fact 
that they can not be verified by repetition without another demag- 

TABLE XXVII. 

Showing the manner in which demagnetized high carbon steel approaches 
the cyclic state under various forces. 



Number of cycle 



Apparent induction 



H=\ 



//=a 



^-5 



/^=i5 






109 
108 

1 

.01 



254 

249 

5 

.02 



796 


3190 


780 


2980 


16 


210 



.02 



.07 



6805 

6680 

125 

.02 



//=40 



1 


109 


254 


790 


3130 


6780 


11660 


2 


109 


254 


795 


3160 


6790 


11670 


3 


109 


254 


796 


3190 


6800 


11670 


4 


109 


254 


795 


3190 


6805 


11680 


5 


108 


254 


790 


3190 


6800 


11680 


6 


108 


252 


785 


3170 


6800 


11680 


7 


108 


252 


785 


3150 


6800 


11670 


8 


108 


250 


780 


3140 


6800 


11670 


10 


108 


249 


780 


3140 


6800 


11670 


20 


108 


249 


780 


3130 


6790 


11670 


50 


108 


249 


780 


3100 


6760 


11670 


100 


108 


249 


780 


3050 


6730 


11670 


200 


108 


249 


780 


3020 


6700 


11670 


400 


108 


249 


780 


2990 


6690 


11670 


600 


108 


249 


780 


2980 


6680 


11670 


800 


108 


249 


780 


2980 


6680 


11670 



11680 

11670 

10 

.00 



Plotted on Fig. 21. 

netization. These reasons apply whether the induction is to be 
measured ballistically or magnetometrically, and if results are to be 
compared by these two methods care must be taken that the induc- 
tions have been measured under the same conditions. 
117.^7—07 — 6 



256 



Bulletin of the Bureau of Standards, 
ONE DEMAGNETIZATION SUFFICIENT. 



[^o/. /,A'o, 2. 



It has been suggested by Searle that the specimen should be 
demagnetized before each determination of an induction. We have 
already shown that after demagnetization the cyclic induction at 

TABLE XXVIII. 

Showing the manner in which low carbon steel approaches a cyclic state 
imder various forces, when it has been demagnetized before each new 
force is applied. 









Apparent induction 






Number of cycle 














H=X 


^=3 


H=A 


^-5 


/f=.7 


^=xo 


Make 


190 


1900 


4200 


6800 


9980 


12460 




191 


1920 


4250 


6890 


10000 


12500 




191 


1910 


4260 


6890 


10010 


12500 




191 


1920 


4270 


6900 


10040 


12510 




192 


1950 


4290 


6900 


10080 


12510 




192 


1970 


4290 


6910 


10080 


12520 




191 


2000 


4300 


6920 


10060 


12520 




190 


2010 


4300 


6920 


10060 


12510 




190 


2010 


4290 


6930 


10060 


12510 




190 


2000 


4290 


6930 


10050 


12510 


10 


190 


2000 


4280 


6930 


10050 


12500 


20 


190 


1990 


4260 


6910 


10040 


12470 


50 


190 


1980 


4250 


6890 


10030 


12470 


100 


190 


1960 


4230 


6850 


10020 


12470 


200 


190 


1950 


4190 


6810 


10010 


12470 


400 


190 


1940 


4160 


6800 


10000 


12470 


600 


190 


1930 


4150 


6790 


9990 


12470 


B^^ 


192 


2010 


4300 


6930 


10080 


12520 


max 
^fl„^, 


190 


1930 


4150 


6790 


9990 


12470 


■*^nnal 


2 


80 


150 


140 


90 


50 


^nnal 


.01 


.04 


.04 


.02 


.01 


.00 



any magnetizing force is not affected by any preceding application 
of smaller forces; but as this is an important detail of manipulation 
it is desirable to leave no uncertainty. Two sets of data were there- 



Burrtnvs.^ 



Method of Demagnetizing Iron, 



257 



fore obtained— one for a single demagnetization and another in which 
the specimen was demagnetized before each measurement of the induc- 
tion. The two sets of data are given in the Tables XXVI and XXVIII. 







% 






























14600 


^ 














































H 


=10 


















12800 




































V 














































H 


=5 


















11000 


































10900 


V 


v^ 






























ifMnn 








-^ 


.^ 






































H 


^■3^ 


— 
































9200 


































9100 


\ 
































9000 




^ 






























8900 










■^^ 







■ 


- 






























H 


= 2 


















<MftAn 


/\ 
































5800 




N 


X, 




























5200 






"^ 


^^ 


^^ 






































H 


^ 

































1800 


t 
































1200 














H 


=o:5- 





















































100 200 300 

B NUMBER OF CYCLE »- 

Fig. 19. — Showing the manner in which detnagneiized iransformer iron approaches 
the cyclic state for various values of IL 

(Numerical data in Table XXV.) 

The final values of the induction are the same in each case, and the 
main characteristics of the manner of approach to the cyclic state 



258 



Bulletin of the Bureau of Standards. 



[ Vol. 4, No. 2, 



are maintained in each. Whatever differences there are occur in 
the earlier reversals. This is another argument in favor of the final 
value as the normal one. 































— r 

1 






14200 




































r— 














H = 15 
















12500 


































Sy^ 
































12400 
















H=1C 




















































'N— 
































10000 
















H=7 






















































r-^ 
































6800 


\ 








— ' 


■ . 


r- 




















6800 
















H^O 


















4300 
4200 


































r^ 








«_ 






































H=4 


















2000 


































r 
































1900 












H = 3 


















































200 


































100 
















H=1 


















































t 

B 










1 


00 

N 


UMBE 


ROFC 


:ycle 


2 


00 








8 


00 



Fig. 20. — Showing the manner in which demagnetized low carbon steel approaches 
the cydic state for various values of H, 

(Numerical data in Table XXVI.) 



Burrows.^ Mcthod of Demagnetizing Iron, 259 

EFFECT OF VISCOSITY. 

Fig. 22 shows the manner of approach to the cyclic state under 
two circumstances. The upper curve shows how a specimen of 







































































11700 


































































11600 
















H=4 





















































6600 






































— 


— 




. 






































H=l 


5 
















SI on 


fV 


_^ 






































■ 














, 


' 




























-H^1 


U 
















800 


































































7AA 
















H=5 




















































800 




































































200 
















H=2 




















































200 


















































































H = 1 



















T 100 200 800 

B NUMBER OF CYCLE 

Fig. 21. — Showing the manner in which dentagnetized high carbon steel approaches 

the cyclic state for various values of H. 

(Numerical data in Table XXVII.) 

high carbon steel comes to a cyclic state on repeated reversals of the 
magnetizing force by hand switch. The solid portion of the curv^e 



26o 



Bulletin of the Bureau of Standards. 



IV0I4.N0.2. 



just below this shows apparent inductions as actually observed after 
imperfect demagnetization. Between the solid portions of this curve 
reversals were made quite rapidly — ^several times per second. The 
dash lines give the hypothetical curve the apparent induction would 
have followed if the apparent induction had been measured for each 
reversal and no rapid reversals had been made. There are two 
causes of irregularities in the curve showing the manner of approach 



S1U0 












































r 


\^ 










































^ 




*^ 




































K 










































' N 


\ 














^oj 


la/c 


^e 


o^a/ 


















^ 






-. 


y^ 
















^-2i 




Chi 


L^ 


[icsi 


ate. 








03000 








\ 


^^^ 


•--. 


^ 





























z 














f 






'7" 


=^ 





















Z 
111 


























y'^ 






"-" 


"? 






— 


a: 

t 














































V 


a 










































*^S 






b 


































Sho 


ivinf 


effe 


;tof 


y 

a pa 


jse 


■ — 






























WO 

the 


rap 
ippa 


d re 
rent 


'ersi 
indt 


Is (6 

ctio? 


on 
>as 
































sub 


seqi. 


enti} 


' me 


isur 


»d 





























200 



400 



600 800 

NUMBER OF CYCLE 



1000 



1200 



Fig. 22. — Showing how the manner of approach to the cyclic state in high carbon 
steel is modified by rapid reversals of the magnetizing force and by 
long pauses. 

to the cyclic state. A pause at any point in the curve causes the 
apparent induction of the succeeding reversal to be a little larger 
than the one immediately preceding. This is most pronounced in 
the softer materials and for any specimen is greatest in the steep 
part of the induction curve and disappears almost completely in the 
upper parts of this curve. It is noticeable even after the iron has 
reached a cyclic state under normal conditions. The phenomenon 
may be attributed to magnetic viscosity. The connection is made 
clear from the following figure. (Fig. 23). Suppose the iron 



BurfowsA 



Method of Demagnetizing Iron. 



261 



has been subjected to forces oi -^ H and — H alternately at the rate 
of one reversal per second. Then it will trace a hysteresis loop 
having its vertices at two symmetrical points as A and B. If, how- 
ever, the reversals are interrupted when the iron is at the point A, 
the steady application of the force will cause the induction to creep 
from A to A'. After this creeping has ceased a reversal of the mag- 
netizing force will bring the state point down to B. A further pause 
will again show a creeping from B down to B', which is symmetric 
with A'. A magnetometric measurement would take account of 
this creeping and would measure the induction Oa'. A ballistic 
measurement however would indicate only the portion Oa, the 
remainder aa' being lost 
on account of its slowness. 
This is on the assumption 
that a ballistic galvanome- 
ter with sufficient torsion 
in its suspension to bring 
its movable system back to 
zero is used. An instru- 
ment whose movable sys- 
tem has no directive force, 
such as the Grassot flux- 
meter, would measure the 
full induction as com- 
pletely as the magnetome- 
ter. However, even with 
an ordinar}'' ballistic galva- Fig. t:^,-— Ideal curve to illustrate the effed of 
nometer this full induction ^nagnetic viscosity on the apparent induction. 

can be determined. Let a ballistic deflection betaken when the iron is 
traversing the cycle AB. This will be proportional to ba. After 
a pause take the deflection on the return reversal. This will be pro- 
portional to a'b. The second deflection exceeds the first by aa', 
which is the amount of creeping at one end of the cycle. The full 
induction would therefore be proportional to ba+2aa'. As this 
creeping is greatest in the steep part of the B-H cnrw^ a single deter- 
mination here will tell whether it is of sufficient magnitude to war- 
rant consideration. In some of the irons measured it has amounted 
to as much as i per cent. 




262 



Bulleitn of the Bureau of Standards, 



[ Vol. 4, No. 2, 



Another irregularity in the curve showing the manner of approach 
to the cyclic state is the peculiar effect of several rapid reversals. 
After such treatment the first inductions are too low, then the suc- 
ceeding ones are too high, but after some slow reversals the induc- 
tions show no sign of irregularity. The two kinds of irregularity 
are shown graphically in the lower comer of Fig. 22. 



600 
490 
480 
470 
460 

^0 
§ 440 
1430 

£420 
< 




ra 






































\ 














1 


























V 








































\ 


s, 








































'^ 


^». 
































■^ 


*~^ 


>--< 


1 




^ 


"t^ 


































^-< 


M 


>--< 


^ 


^^ 


^^ 


■vn 






































^ 


M 


P^ 




^^^ 












































"^ 





1 









8: 410 

400 
390 
880 
870 








































--I 





























































































































8 9 10 11 12 13 14 
NUMBER OF CYCLE 



15 16 17 18 19 20 



Fig. 24. — Showing the manner in which a highly polarized bar of low carbon steel 
approaches the cyclic state on repeated reversals of a force H ^2, 

(Numerical data in Table XXIX.) 
EFFECT OF REPETITION. 

One might suppose that a sufficient number of reversals of the 
magnetizing force would obviate the necessity of demagnetization. 
This is not the case, however, as is seen from the manner in which 
a specimen of low carbon steel approaches the cyclic state after 
intense polarization by a force of 100. The data for this experiment 
are shown numerically in Table XXIX and graphically in Fig. 
24. The inductions on successive reversals do not form a smooth 
curve as those obtained after complete demagnetization would, but 



Burrows.] 



Method of Demagnetizing Iron. 



263 



those inductions obtained by reversing the magnetizing force from 
the direction in which the strong polarization was applied are 
greater than those due to either the preceding or the following 
reversals in the opposite direction. Thus Fig. 24 shows two 
lines, converging after about twenty reversals. As the reversals 
continue the apparent induction becomes gradually smaller, differing 

TABLE XXIX. 

Showmg the manner in which a highly polarized piece of low carbon steel 
approaches the cyclic state. 





Polarizing force, 


too; Cyclic force, a 




Number of cycle 


Apparent induction 


Number of cycle 


Apparent induction 


l(make) 


2500 


7i 


438 


1 (reveree) 


446 


8 


429 


1 i (reverse) 


495 


8i 


437 


2 


443 


9 


427 


2i 


470 


n 


430 


3 


441 


10 


425 


3i 


460 


10 i 


427 




438 


20 


409 


4i 


452 


20 i 


409 




435 


50 


388 


5i 


447 


100 


376 




433 


200 


370 


6i 


442 


1200 


370 



431 



Normal induction 



680 



Plotted on Fig. 24. 

more and more from the normal induction. After 200 cycles (400 
reversals) the apparent induction has reached a minimum which a 
thousand double reversals do not alter. In another case a bar of 
polarized iron was subjected to slow reversals of the magnetizing 
force for four hours and yet showed no increase in the apparent 
induction. 



264 



Bulletin of the Bureau of Standards. 
STRONG VIBSATIONS. 



[Ko/./.Ab.i. 



While the study of magnetism was yet in its infancy Gilbert dis- 
covered that a soft iron bar could be quite strongly magnetized by 



1 














1900 






























1800 






























1700 














/ 
















1600 














/ 




1 
















Tsob" 


— 














7 


^ 




1 












1400 












/ 






i 












1300 












/ 


















1200 










/ 




















1100 










/ 




















1000 








/ 


J 








j 




1 








900 








/ 






















800 






/ 


/ 








i 




\ 










700 






/ 










\ 




\ 










600 






/ 










\ 




\ 










600 




/ 












\ 


\i 


\ 


) 








400 




/ 














% 




V^. 


W 






300 


/ 


1 
1 














j\ 


\ 


\ 


\ 






200 


/ 


1 

1 
1 
















\ 




\ 




t 

y 


100 


/ 


1 • 

1 

I 


















\ 


V 


V. 




/ 




1 
1 
1 












i 


5 

)ISTA 


MCE(£ 


m)FR 


.1 
OMA. 


i(IS=r 


^ 


1 s 


i 

AMPL 


\ K 
ITUDE 


> { 




1 


2 V 


s 



Fig. 25. — Theoretical curves based on Heain sides' s formula showing how the ampli- 
tude of an alternating magnetic flux varies over the cross section 0/ a 
round rod for various assumed values of the permeability. 

holding it in the earth's field and striking it a sharp blow with a 
hammer. A soft iron wire placed in the terrestrial field and gently 



Burrows.] 



Method of Demagnetizing Iron, 



265 



rubbed takes up a magnetization far greater than its penneability 
determined in the usual way would indicate. Equally gentle rub- 
bing will remove the major portion of the most intense residual 
magnetization. Ewing^' has investigated quite thoroughly the effect 
of intense mechanical disturbances on the magnetic state of a bar of 

TABLE XXX. 
Showing the increase of induction in soft iron due to very gentle vibration. 



H 


B 

Normal 


B 
With tapping 


Increase of B due 
to tapping 


Per cent 
increase of B 


.2 


200 


211 


11 




.3 


370 


395 


25 




.4 


600 


645 


45 




.5 


950 


1018 


68 




.6 


1445 


1542 


97 




.7 


2400 


2525 


125 




.8 


3400 


3535 


135 




.9 


4200 


4340 


140 


3 


1.0 


4850 


4985 


135 


3 


1.1 


5400 


5525 


125 


2 


1.2 


5900 


6010 


110 


2 


1.3 


6350 


6440 


90 


1 


1.4 


6700 


6770 


70 


1 


1.5 


7050 


7100 


50 


1 


1.6 


7350 


7380 


30 





1.7 


7600 


7620 


20 





1.8 


7850 


7860 


10 





1.9 


8100 


8105 


5 





2.0 


8300 


8300 









Plotted on Fig. 26. 

iron. The effect of vibration is to shake in more induction if the 
magnetic force is acting, and to shake out the residual induction if 
no magnetic force is acting. The hysteresis loop is contracted and 
draws in close to the induction curve, which loses its point of inflec- 
tion and apparently starts out with a maximum permeability which 



*® Magnetic Induction, etc., pp. 77 and 84. 



266 



Bulletin of the Bureau of Standards. 



[ybl. 4, No. ». 



steadily decreases. While the increase in permeability is appreciable 
in moderately strong fields, it is in weak fields that the effect is most 
striking. In the case recorded by Ewing and which we have no 



10000 


























































,^ 






9000 






















y 


y 








8000 




















y 


y 


























/ 


/ 












7000 
















/ 


/ 


























y 


/ 
















6000 












r 


V 




























.£/ 




















5000 










^ 


s'/ 




























// 






















4nnn 










































/ 






















8000 








1 
























































2000 






































1 






















150 


1000 






1 


/ 


1 


^ 


^-^.x 
















100 


t 

B 




J 


// 








^ 


R^l'c 














60 


.^ 


^ 












vS 


^ 


s^ 














1 


rr 


















z 








\ 



Fig. Ub.— Showing the influence of gentle znbrations on the inductions in soft iron, 
(Numerical data in Table XXX.) 

reason to suppose was unusual the permeability as measured during 
a mechanical vibration assumed the enormous value of 8o,ooo. 
These same phenomena are observed in hard iron and steel, but to 
a much less degree. 



Burrows.] Mcthod of Demagnetizing Iron, 267 

GENTLE vibrations! 

The following experiment was undertaken to determine whether 
the ordinary vibrations of a building containing moving machinery', 
such as a reciprocating engine, affect the values obtained in a mag- 
netic test. The gong was removed from a small electric bell and 
the electromagnet mounted so that the hammer might strike against 
one end of a slender wooden rod 50 centimeters long, the other end 
of which rested against one of the yokes containing the test speci- 
men. The wooden rod was interposed partly to deaden the effect of 
the blows delivered by the hammer and partly to permit the removal 
of the electromagnet to such a distance that its field would not react 
on the test specimen. To diminish the vibration still further a 
piece of soft rubber tubing was slipped over the hammer and 
another piece fastened to the end of the wooden rod. To insure a 
separation of the natural vibrations of the building from those of 
the experiment, the magnetic system under test was mounted on 
several layers of heavy wool felt. As nearly as could be estimated, 
by placing the hand alternately on the apparatus under test and on 
the table, the tapping device gave a disturbance of the same order of 
of magnitude as the vibration of the building. With this arrange- 
ment the data of Table XXX were obtained. The first column gives 
the magnetizing force ; the second, the value of the induction after the 
iron had been subjected to many reversals to insure a cyclic state; 
the third, the induction obtained while the iron was under vibration ; 
the fourth, the increase due to vibration, and the last column gives 
the proportional increase. These data are shown graphically in 
Fig. 26. It is to be noticed that the effect of vibration, both in 
absolute value and in percentage, passes through a maximum at 
approximately the point where the differential permeability is a 
maximum. The maximum value of 7 per cent in the disturbing 
effect shows that for accurate work it is necessary to protect the 
apparatus from vibration. Even the slamming of a door at one time 
and the dragging of a heavy box along the floor at another have 
modified the induction by a measurable amount. 

Small changes in the intensity of the mechanical disturbance were 
accompanied by correspondingly small changes in magnetism, so that 
the curve may be taken as that characteristic of small disturbances. 



268 Bulletin of the Bureau of Standards. [ voi. 4, No. 2, 

To investigate more fully the nature of the effect of these 
mechanical vibrations the specimen was subjected without vibrations 
to many reversals of a small force until a cyclic state ensued and the 
ballistic throw on reversal noted. Next, without altering the cur- 
rent, the vibrator was started. This produced a small deflection. 
The return reversal was then taken without vibration, then another 
reversal without vibration, then the tapping, and lastly a reversal 
while the tapping was in progress. The following table. shows the 
results: 



Operations 


performed 


Galvanometer 


Mai^netic. 


Mechanical. 


Deflection. 


Reversal. 


None. 


+7.00 


None. 


Tapping. 


-f .23 


Reversal. 


None. 


-7.28 


Reversal. 


None. 


+7.00 


None. 


Tapping. 


-f .29 


Reversal. 


Tapping. 


-7.47 



The small deflection produced by tapping after a reversal had been 
made was the result of the first few taps, for an instantaneous closing 
of tapping circuit produced the full effect which was not increased 
by repeated and continued tapping. It is also characteristic that a 
single reversal wipes out the effect of previous tapping so that the 
second reversal is normal. What occurs m: / be shown more clearly 
by the use of Fig. 28. Here A represents the magnetic state 
before the first throw. The first reversal brings the state point to 
B. Tapping runs it up to D. A reversal without tapping brings 
it back to A. Tapping nms it down to C. Reversal with tapping 
carries it to D. So that simple reversals cause the state point to 
traverse cycle AB. Reversals with taps give cycle CD. Reversals 
followed by taps give cycle CBDA. 

A comparison of these effects with those noted under the study 
of viscosity shows a close connection between the creeping up of the 
induction due to viscosity and the same thing for tapping. Both 
these phenomena may be accoimted for by assuming a frictional 
force opposing the movements of the molecular magnets. It was 
found that such gentle vibrations as these were of little help in 
demagnetizing either when used alone or with current 



burrows.] 



Method of Demagnetizing Iron. 



269 



For higher inductions the eflFect of tapping was appreciable but 
negligible. 

The persistance of previous polarization, as modified by a slight 
tapping, is shown in the data of Table XXXI. Here the iron has 
been polarized and then subjected to reversals of a small force till a 
cyclic condition exists. A few taps raise the apparent induction, 
which then decreases to a second constant value somewhat higher 

TABLE XXXI. 

Showing the demagnetizing effect of tapping combined with repeated 

reversals. 



Number of reversal 


Galvanometer deflection 


1 


9.80 


2 


6.19 


3 


5.99 


4 


5.81 


6 


5.71 


8 


5.66 


10 


5.62 


20 


5.62 


100 


5.61 


200 


5.62 


202 


5.80 after gentle tapping for 15 seconds 


204 


5.86 " " " " 1 minute 


206 


5.89 '' '' '' '' 2 " 


306 


5.89 " " " " 100 cycles 


406 


5.69 


500 


5.69 


1800 


5.69 



than the first. The gentle vibration has therefore removed a por- 
tion of the residual induction, but is not an efficient means of 
demagnetization. 

From the preceding experiment it appears desirable that the 
magnetic system be protected from small mechanical vibrations. 
A pad of felt half an inch thick accomplishes this very nicely for 
all ordinary cases. 



270 



Bulletin of the Bureau of Sia7idards, 
TNFLUENCE OF TEMPERATURE. 



[ Vol. /. No. 2. 



It is well known that for a small rise of temperature above room 
values the permeability of iron increases for low inductions and 

TABLE XXXII. 

Showing the induction at various temperatures of an annealed transformer 

iron ring. 



H 


B^ 
/=8 


/=aS.5 


^48 

/=48 


^48-^6 


40 


Bi^—Bi 
40^8 


0.5 


473 


495 


516 


43 


-f-1.1 


.0023 


1.0 


3317 


3479 


3621 


304 


+7.6 


.0023 


2.0 


8810 


8970 


9170 


360 


-f9.0 


.0010 


3.0 


11560 


11700 


11870 


310 


+ 7.7 


.0007 


5.0 


14330 


14460 


14510 


180 


-f-4.5 


.0003 


10.0 


16440 


16440 


16440 








.0000 


15.0 


17150 


17160 


17180 


30 





.0000 



See Fig. 27. 



TABLE XXXin. 



Showing the inductions at various temperatures of an unannealed trans- 
former iron ring. 



H 


^12 
/=ia 


B„ 


-^47 — -^18 


Bv~Bx^ 
35 


-^47— -^15 

35 ^iV 


0.5 


290 


306 


16 


.5 


.0017 


1.0 


1081 


1148 


67 


1.9 


.0018 


2.0 


4670 


4800 


130 


3.7 


.0008 


3.0 


7225 


7310 


85 


2.4 


.0003 


5.0 


10290 


10340 


50 


1.4 


.0001 


10.0 


13930 


12920 


—10 


- .3 


.0000 


15.0 


15630 


15590 


-40 


-1.1 


.0000 


See Fig. 2; 


1. 











decreases for high inductions. At higher temperature this temper- 
ature coefficient is always negative and increases rapidly with the 
temperature, until finally the iron becomes practically nonmagnetic 



Burrows.] 



Method of Demagnetizing Iron. 



271 



at some temperature between 690° C. and 870° C. For the ordi- 
nary fluctuations of room temperature very little experimental work 
has been done. 




t 



10 11 12 18 14 15 



1 2 
H— *^ 

Fig. 27. — Showing the effect of temperature and annealing on the induction in soft 

iron, 
(Numerical data in Tables XXXII, XXXIII, and XXXIV.) 

Ewing," from data obtained at 7° and 100® C, concluded that 
atmospheric fluctuations need not be considered in magnetic meas- 



^ Magnetic Induction, etc., p. 178. 



11737—07- 



272 



Bulletin of the Bureau of Standards. ivol 4. No. 2. 



urements. Permanent magnets such as are used in magnetic surveys 
and in electrical measuring instruments have a negative temperature 
coeflScient of the order of .05 per cent. Whether or not the temper- 
ature coefficient is of sufficient importance to warrant its considera- 
ation is a question of the degree of accuracy desired. It seemed 
worth while therefore to determine the temperature coefficients of a 
few specimens over the atmospheric range. Four different speci- 
mens of transformer iron were examined at different temperatures. 
A portion of the data is shown numerically in Tables XXXII, 

XXXIII, and XXXIV, 
and graphically in Fig. 27. 
These specimens were two 
bundles of stamped trans- 
former iron rings about 10 
centimeters in diameter, cut 
from the same sheet. One 
was annealed and the other 
not. From the data and 
curves the following obser- 
vations may be made: 

(i) The change in in- 
duction per 1° C. rise in 
temperature is greatest in 
the neighborhood of the 
maximum permeability. 

(2) The temperature co- 
efficient is greater for the 
annealed than for the un- 
annealed iron. 

(3) The high value of this maximum temperature coefficient (one- 
fourth per cent) shows that temperature must be taken account of 
if an accuracy of i per cent is to be attained. 

(4) The increase of induction due to annealing is greatest near 
the point of maximum permeability. 

Throughout this work one is impressed with the varying sensi- 
tiveness with which the different parts of the B-H curve are influ- 
enced by slight changes in the conditions. All those elements, 
such as polarization, temperature, viscosity, or vibrations, which 




Rg. 28. — Ideal curve to illustrate the effect of vi- 
bration on the apparent induction. 



Burrows.'] 



Method of Demagnetizing Iron, 



^75 



tend to modify the apparent induction produce their greatest effects 
in the steep part of the induction curve. Beyond the critical point 
the induction is independent of previous magnetization and but 
lightly influenced by vibrations and temperature changes. Greater 
sensitiveness is noticed in the soft irons than in the hard ones. The 
difficulties of permeability measurements, therefore, are found in the 
earlier part of the induction curve, and it is here that the greatest 
care must be taken and the largest tolerance allowed. 

TABLE XXXIV. 

Showing the effect of annealing on the induction m transfonner iron 
(Temperature lO^C). Calculated from Tables XXXII and XXXIH. 



Jf 


Annealed »^a 


Unannealeda>i?tt 


Ba-Bu 


Ba-Bu 
Ba 


0.5 


475 


289 


186 


.39 


1.0 


3332 


1078 


2254 


.67 


2.0 




4660 


4170 


.47 


3.0 


11580 


7220 


4360 


.38 


S.O 


14340 


10290 


4050 


.28 


10.0 


16440 


13930 


2510 


.15 


15.0 


17150 


15630 


1520 


.09 



See Fig. 27. 



THE BEST METHOD OF PROCEDURE. 



In view of evidence offered in the preceding pages the following 
rule may be outlined as the best (ballistic) method of procedure in 
magnetic testing: 

The magnetic system, consisting of the test pieces and the con- 
necting yokes, should be mounted with its plane perpendicular to 
the earth's field. If necessary the system should be protected from 
mechanical vibrations by means of a pad of felt, or something equiv- 
alent. If an accuracy of i per cent in the steep part of the B-H 
curve is desired the temperature should be kept at some standard 
temperature (e, g., 20° C.) constant to i ° or 2° C. It is not feasible to 
apply a temperature coefficient correction on account of the diffi- 
culty in getting its value. 



274 Bulletin of the Bureau of Standards. [yoi. a, jvo. i. 

The demagnetization should be accomplished by a current 
reversed at the rate of approximately one cycle per second, while 
gradually diminished in such a way that the rate of decrease of the 
induction is as nearly as may be uniform. An ammeter in circuit 
and a rough estimate of the shape of the B-H curve will enable one 
to regulate the rate of decrease of current with sufficient exactness. 
The initial demagnetizing current should be sufficient to carry the 
induction beyond the knee of the B-H curve," and the final current 
should be not greater than the smallest magnetizing current to be 
used. 

The full demagnetization may be accomplished in about ninety 
seconds. 

Now apply the lowest magnetizing force desired and reverse at 
the same speed as in demagnetizing. At intervals get a ballistic 
deflection. Continue this until two deflections about twenty-five 
reversals apart show only a negligible difiEerence*\ This final deflec- 
tion is the normal induction. 

Without demagnetizing again, apply the next larger magnetiz- 
ing force and reverse as before. Continue in this way till all the 
required points on the curve have been obtained. 

In closing I wish to acknowledge my indebtnesss to Professor 
Rosa, under whose supervision the work has been done, for his con- 
tinued advice and suggestions. 

Washington, September 3, 1907. 

^ Without going to the trouble of a preliminary test an initial demagnetizing force 
of 15 units may safely be assumed for all specimens of soft iron. 

" Several hundred reversals may be required in the steep part of the B-ff carve, 
whUe half a dozen are sufficient in the upper portions. 



A DEFLECTION POTENTIOMETER FOR VOLTMETER 

TESTING. 



By H. B. Brooks. 



1. INTRODUCTION. 

In a former paper* the writer derived an expression for the cur- 
rent through the galvanometer of an unbalanced potentiometer, used 
in connection with a volt box, and showed how this formula could 
be applied to the design of a class of instruments, for current and 
voltage measurements, having properties intermediate between those 
of the balance type and of the deflection type. A description was 
given of an instrument constructed on this principle, which was used 
for measuring voltage in photometric work, and which has now 
been in service for the past two years, giving satisfactory speed and 
accuracy. 

The object of the present paper is to give some further modifica- 
tions of circuits which may be used for this purpose, with their 
advantages and defects; to show what features should be incorpo- 
rated in an instrument of this kind for such work as the testing of 
voltmeters, and to describe an instrument of this type recently con- 
structed. This has been designed for voltmeter testing and other 
precision measurements of voltage in the laboratory and testing room. 

2. A STANDARD INSTRUMENT FOR VOLTMETER TESTING. 

An instrument to be used as a standard for voltmeter testing 
should first of all be accurate, permanent, and unaflFected by mag- 
netic fields and similar disturbing influences. This requires that the 
bulk of the unknown voltage be measured by the potentiometer 
method, as no known type of voltmeter, not even so-called " laboratory 
standard " instruments, will meet the above requirements. In order 

*This Bulletin, 2, p. 225; 1906. , 

275 



276 Bulletin of the Bureau of Standards, iroi. 4. No. 2. 

to save time and avoid the necessity for extreme steadiness of the test 
voltage, a small portion of the quantity should be measured by the 
deflection of a galvanometer. This galvanometer should be a piv- 
oted instrument, of good working qualities, and should have a sen- 
sibility such that one division of its scale corresponds to say one- 
tenth to one-fifth of a scale division of a voltmeter of the same max- 
imum range as the potentiometer. This gives great ease of reading, 
as it is usually sufficient to read the galvanometer to the nearest di\'i- 
sion, neglecting tenths. These requirements indicate a deflection 
potentiometer, and as a number of variations are possible, in the 
arrangement of circuits for such an instrument, these various plans 
will be examined with a view of determining the one which is the 
most suitable. 

It is desirable that the standard instrument be semiportable, for 
while such an instrument is commonly used in one place, it is often 
necessary to make precision measurements in other places on rela- 
atively short notice. In the case of the deflection potentiometer, 
by building the pivoted galvanometer in as a part of the apparatus, 
the only accessories are the storage battery and the standard cell; 
the former must be carried separately, and preferably the latter also. 

3. ARRANGEMENTS OF CIRCniTS. 

In plan i (see page 231, former article) the volt box ratio is 
constant, and the setting is made on the potentiometer wire. The 
arrangement of circuits may be seen from Fig. 4 of this article by 
omitting the resistance r^; the symbols used correspond with those 
of the previous article. The difficulty with this plan lay in the fact 
that the compensating resistance in the galvanometer circuit, r^, was 
a function of two variables, the resistance of the potentiometer wire 
up to the setting, r„ and the regulating rheostat in the storage cell 
circuit, ^8, no satisfactory way of providing this double compensa- 
tion being available. To avoid this difficulty plan 2 was devised, 
in which r^ is a constant ; r^ therefore compensates only for changes 
in 2r (the total resistance in the galvanometer circuit) due to varia- 
tions of r,. The setting is then made on the volt box, and a com- 
pensating resistance r^ is arranged to take care of variations due to 
changes of the setting. This plan was adopted for the first instru- 
ment of this type, in which the range was from 95 to 125 volts. 



Brooks.] 



A Deflection Potentiometer. 



277 



A third plan, suggested by Dr. M. G. Lloyd, is like plan 2, except 
that instead of a constant total resistance R between the emf. ter- 
minals of the volt box, with the drop taken from a variable fraction 

- of this, the drop is taken from a fixed resistance and R is variable, 

as shown in Fig. i. 



r-Hllh- 



-^wvwv 



/W\AAAA/WW^^ 



(7> 



wwwwwwwwvv-' 



-a/wwwwwna/Saaaaaaaaaaa/V 



rAAAAAAAAA/WWWV 



k 

Rg. 1. — Third plan of circuits. 

The equations for this case are the same as for plan 2. R ^"T 

is more nearly constant in plan 3 than in plan 2. A serious disadvan- 
tage of plan 3 is the fact that R^ the resistance of the volt box, is 
low on low settings. If the instrument reads down to a small frac- 
tion of the maximum, and through mistake the maximum pressure 
is applied while the dial is set at or near the minimum, a current 
many times greater than normal will flow through the part of the 
volt box in circuit, with consequent damage. 

Plans 2 and 3 have the disadvantage of variable damping of the 
galvanometer. For an instrument of limited range (as 95 to 125 
volts) this disadvantage practically disappears. By designing the 
coils so that the value of 2r for the mean setting is equal to the 
total resistance for critical damping of the galvanometer, the damp- 



278 



Bulletin of the Bureau of Standards. \voi. 4. J^o. 9. 



ing will still be such as to give good working, even at the extremes 
of the range. If, however, we are to cover a wide range with an 
instrument using plan 2, it is necessary to modify the circuits so as 
to preserve critical damping over the whole range. This may be 
accomplished by the arrangement shown in Fig. 2. 



r-Hi|H 



^\AAAAMM/WWWYWWWWW\/W\AA/\AA/^^ 



|l|J~~i 



P-1 




^ -VW\AAAAAAA/OwW\AA/WWWV 



Rg. 2. — Fourth plan of circuits. 

This arrangement is the same as plan 2, with the addition of a 
variable shunt r, to the galvanometer, which is changed at the same 
time as the compensating resistance r^. Since r^ and r, are inde- 
pendent variables, we may impose two conditions: (i) The current 
through the galvanometer, for all settings, must be such that one 
volt JE (diflFerence between p times the setting and the applied 
voltage E) will give a deflection of m scale divisions; (2) the resist- 
ance of the damping circuit must be constant and equal to r^, the 
total resistance for aperiodic damping. In the former article it 
was shown that if 2r is the total resistance in the galvanometer 

circuit, (neglecting all electromotive forces) — the fractional part of 

the volt box from which the drop is taken, m the number of scale 



Brooks.} 



A Deflection Potentiometer. 



279 



divisions which the galvanometer is to give for one volt unbalanced 
emf . in the pressure to be measured, the value of 2r is given by 
the equation 

pm I . \ / 

If the current / is required by the unshunted galvanometer for 
one scale division, when the shunt r, is applied this is increased to 

By equation (11) we may write for this case 

r» 



2r= 



pnil{r,+rg) 



(12) 



For convenience we may denote the resistance in the galvanom- 
eter circuit, aside from r, and r^, by r'; or 



r' = rr 



r,r. 



rx+r. 



?P-1. 



The damping circuit is then as shown in Pig. 3, and for critical 
damping 




ro-\- 



ry 



= r. 



also, 



h/Wi 



Fig. 3. 
Since 



r.+r' 






By solving these equations we get 

\—pm iTa 



7^ = -" - ^^- 

pmlr^ 



(13) 
(14) 

(15) 
(16) 



^=^+;^+^^+''. 



28o Bulletin of the Bureau of Standards. ivoi. 4. no. 2. 

^=constant+y?^^+r. 

By means of these formulae we may determine the values of r, and 
rj for a given case,* 

r--Hl|h Hill-—. 



^1-^ 



^wvwvwwwwwwwwwwwvwwwwwww^ 



B- 



-r£=1 



♦^*p-* 



iZl! 



*.— 



/\m/wwwwwww\Aaaa/\amaa/v^^ 



^ W\/WWW\AAAAAA/WWWWWWW\/W\A 



<i*-V- 



<.— 



-vwwwvvwww 

n 



\/WWWWWyWNA/^ 



1 ^<,+v*. 

Fig. 4. — Fjl^A jp/fl« of circuits. 

The variable shunt to the galvanometer in plan 4 must be made 
of copper, and should preferably be mounted inside the galvanom- 
eter case, to insure equality of temperature. This would require 
numerous leads from the shunt to the potentiometer, if the galvan- 
ometer is not to be built into the potentiometer. Plan 4 also has 
the disadvantage of requiring a larger number of coils than the 

'The method of arranging the compensating coils rj in Fig. 2 was suggested to 
the writer by Dr. W. P. White, who has recently described it in the Physical Review, 
25, 534, 1907; and in the 2^itschrift ffir Instrumentenkunde, 27, 210; 1907. 



Broois.] A Deflection Potentiometer, 281 

others for a given range and number of steps. A further practical 
disadvantage of plans 2 and 4 is that the sections of the voltbox, 
which require precision adjustment, will nearly all be odd values. 

In considering the features which would be desirable in an instru- 
ment of this class for voltmeter testing, in which the range from 
zero to the maximum is to be covered, and several ranges provided, 
it was found that none of these plans entirely met the requirements, 
and a plan was sought which would be satisfactory. This was 
obtained from plan i by adding a variable shunt to the potentio- 
meter wire AB, which is varied at the same time as r,. This plan 
is shown in Fig. 4. 

In the former article it was shown that for plan i, in which the 
resistance r^ is absent, the current through the galvanometer is given 
by the equation 






(6) 



In plan 5, as r, is increased, r, is decreased ; both of these changes 
tend to lower the fall of potential on AB. By applying KirchhofPs 
laws to this network we get for the value of the galvanometer 
current 



(.,+..+ !i±^..j-.-f 



''«+'•<,+ 






(17) 



RP- 



By comparing this with equation (6) we see that the effect of r^ in 
the first term of the numerator is to make the coefficient of r, 
greater than unity; that is, r, assists r, in lowering the fall of 
potential on AB. The third term in the denominator is seen to be 
r^ in parallel with the sum of r^ and the resultant of r, and r^ in 
parallel. If, therefore, we can choose corresponding values of r, 
and r, so as to keep constant the resultant of these two in parallel, 
while giving the desired regulation of the current through AB, 



282 Bulletin of the Bureau of Standards, \yoL 4. r^o, 2. 

this third term will be a function of r^, since r^ + r, is constant ; r^ 
may then be readily arranged to compensate for this variation, keep- 
ing the denominator, 2r, the total resistance in the galvanometer 
circuit, a constant for all settings and all positions of the regulating 
rheostat r,. It should be noted that if we make re = 00 in equation 
(17), it becomes identical with equation (6). 

The practical limitations of this method should be examined, for 
while negative values of resistance may satisfy an equation, such 
resistances cannot be realized. First, r, cannot be reduced to zero, 

r r 
for this would make the term ' * always equal to zero, and no 

regulation would be possible. It is therefore necessary to have a 
value of ^1, when the cells are giving the lowest emf. at which it is 
desired to use them, which is somewhat greater than the fall of 
potential to be maintained on AB. Let this fall -of potential be 
represented by a; then from a consideration of the first term of the 
numerator in equation (17) we have 



r.+r,+ ^'+;;+^V .= 'j^r^^rii 



r, ' a ^ ' ' '^ 

^T •" "^'^^ ^ ^ 

where r^ is put for r^-^-r^j the resistance of the wire AB. On 
account of the change of emf. of the storage cell, ^^ will vary between 
certain limits, and values of r, and r, must be found for a series of 
values of e^. It is first necessary to find, from equation (11), the 
constants of the galvanometer and assigned or determined values of 
Py niy and H^ how large a value we may allow for the maximum 
resistance between the point of contact on the wire AB and the 
point A. Some resistance should be reserved in a calibrating coil 
in the galvanometer circuit, which may be altered, if necessary, to 
correct for change in the galvanometer sensibility with time. This 
maximum value, r,„, will occur when the slider is at the center of 
the total resistance in the storage cell circuit; that is, when 



Brooks.] A Deflection Potentiometer. 283 

and its value is 

By solving (18) for r, and substituting this value in (19), solving 
for r„ we get 

• «*^_4^ (20) 

Substituting this value of r^ in equation (18) and solving for r,, we 
get 

' «' 4^m ^ \ 

In this equation e^ is the only variable, hence 

r,= constant x e^^ 

which is a very convenient formula to use. 

It is somewhat more convenient to get r„ not by using equation 
(20), but by putting it into the form 

and using this after values of r, have been determined for the various 
steps of the rheostat. 

Examining equation (20), we see that r, will be infinite when 

li^4^, 

e • • o 

except when — is also equal to unity, in which case r,= -. This is 

e /Lr 

not a practical case. When - is less than -^-^^ r, will be negative. 

ct ffff 



284 Bulletin of the Bureau of Standards, [ vta. 4. No, 9. 

In a practical case this can not occur; r^ must be greater than 

^, to allow for regulation, and hence the numerators of the expres- 

4 

sions for r, and r^ will always be positive. As r^ is determined by 

other considerations, we may choose r^ so as to give suitable values 

for r,. Since r^ must be less than 4^^ and greater than — x 4r,», — 

being somewhat less than unity, we may give r^ the mean of the 
two possible values, or 

The value of e^ used in this formula should be the lowest emf. at 
which the storage battery is to be used. It is seen that the nearer 
^1 approaches a^ or the less margin we allow for regulation, the 
narrower are the limits for r^. It is desirable to have each step 
of r^ an even value, as 10, 20, 50, or 100 ohms, so that if the above 
formula gives a value for each step, which is near an even value, 
the even value should be used, making the necessary adjustment of 
values elsewhere. 

In the case of plan 5, the fine adjustment rheostat in the storage 
battery circuit calls for more attention than would usually be neces- 
sary. The steps on the series rheostat in the battery circuit being 
equal in resistance, it would ordinarily be suflBcient to give the fine 
rheostat a resistance equal to or slightly greater than the resistance 
of one step of the main rheostat. In the case of plan 5, however, 
this would not be sufficient. When the coarse rheostat is changed 
one step, both r, and r^ are changed; when the fine rheostat is 
changed, r, only is changed. It is not practicable to use a double 
fine rheostat, such that r, as well as r^ will be changed, on account 
of the large variation in the value of a step in r„ for uniform steps 
in rj. In the instrument about to be described the change in the 
shunt resistance r, is more eff ^tive in changing the current through 
the potentiometer wire than the change of r,, and to produce, by a 
variation of r, alone, an effect equal to that due to changing r, and 
r„ requires a relatively large change in r,. 



Brooks.] A Deflection Potentiometer. 285 

Let a fine adjustment rheostat r, be connected so as to form a con- 
tinuation of r, (Fig. 4). The current through the wire AB, when no 
current flows through the galvanometer, will be, by equation (17), 



z=- 



r.+^^V. 



(24) 



If we reduce r, by one step, ^r„ increasing r, by ^r,, the current 
will increase. The insertion of the fine rheostat r, in series with r, 
should reduce the current to the original value; hence. 



from which 






r. = ^r3+--^^^ (25) 



This shows that r, must always be greater than ^rj, unless r, be 
made infinite, which gives plan i. The expression also shows that 
the amount by which r, is in excess of Jr^ will increase with increas- 
ing r„ r^, and ^r,, and decrease with increasing r,. It will be found 
that the value of r, for a given instrument will not be the same at 
all points of the coarse rheostat. In the present instrument, r, 
should be 7.5 ohms when the coarse rheostat is in the position of 
maximum r„ and 10.4 ohms for minimum r,. It is desirable to 
have a small amount of overlap, hence this rheostat was made of 11 
ohms resistance. 

It is often desirable to use an external resistance or "multiplier " 
to increase the range of a voltmeter. The same thing can be done 
with the deflection potentiometer, though not with the same facility 
for every plan. With plans i and 5, an external multiplier can be 
used to increase the range, with a small (usually negligible) error 
which is a constant per cent of the deflection reading, for any set- 
ting of the main dial. This may also be done with plan 2, if the 
range is not great; but the relative error in the deflection then varies 
with the setting, being inversely proportional to^. It is impracti- 
cable to use a multiplier with plan 3, as the resistance of the mul- 
tiplier would have to change with the setting, so as to be always the 



286 



Bulletin of the Bureau of Standards, 



\^V<a, 4' No^ 2. 



same multiple of the variable R. The general expression for the 
error involved in the use of an external multiplier is given in a later 
paragraph. 

It will be seen that plan 5 is the most suitable one for a standard 
instrument for voltmeter testing, having the most practical points 
of advantage in construction and operation. The volt box resistance 
is high and constant; the resistance of the galvanometer circuit is 
constant, and the galvanometer may thus be critically damped at all 
settings, without the use of shunts. The steps on the main dial are 



4. DBSCRIPTION OF INSTRUMBNT. 



STORAGE B. 



STANDARD CELL 

9- -Kp 




M/W-AA/WW 

297.50 15X1.6Q 

Fig. 5. — CormscUons of potgnthmeter {dicigrammatic), 

equal resistances, and by suitable design may also be made even 
values, which facilitates checking and adjusting. Multiple ranges 
are readily provided, and if it is desired to measure pressures in 
excess of the highest for which the instrument is built, this may be 
done by the use of an external multiplier, giving a very small but 
constant percentage correction to the deflection reading. 

An instnmient has been designed in accordance with plan 5, for 
use in voltmeter testing in the Bureau of Standards. A diagram- 
matic plan of connections is given in Fig. 5. 



Brooks.] A Deflection Potentiometer, 287 

The main dial has 25 steps of icx) ohms each. This is in series 
with a coil of 9.4 ohms and a dial of 10 steps of .05 ohm each. 
The Weston standard cell is balanced around 509.4 ohms plus the 
amount on the dial, and as the standard current is .002 ampere, cells 
of 1. 01 88 to 1. 01 98 volts may be used, and if need be, this range 
may be varied by changing the 9.4 ohm coil. In the storage cell 
circuit is a series rheostat whose minimum resistance is 297.5 ohms, 
increasing from this value in 15 steps of 1.5 ohms each. This is r, 
of the preceding discussion. At the same time that r, is increased, 
the resistance in shunt to the potentiometer wire, r„ decreases from 
a maximum of 6,814 ohms to a minimum of 2,667.5 ohms. A 
fine rheostat of 1 1 ohms in the battery circuit covers any step of 
the coarse rheostat, and has a compensating resistance of 7.5 ohms 
maximum in the galvanometer circuit. 

The drop is taken from the ends of a 500 ohm coil, which is in 
series with 1 2,000 ohms when the range switch is set on x i. When 
this switch is at x 2 and x 5 the total resistance between the emf . 
posts is 25,000 and 62,500 ohms, respectively. All of these coils, 
except the first 500 ohms, are mounted within and well insulated 
from a brass box which entirely encloses them. The negative emf. 
terminal post is inside of, and well insulated from, a brass sleeve 
which projects into the box and is soldered to it. This box is con- 
nected by a wire to the positive emf. post, and acts as a " guard 
wire " to prevent leakage currents from flowing through the circuits 
of the potentiometer proper. This is a very important precaution, 
which will be appreciated when we consider the high pressure (625 
volts) available for producing leakage, and the fact that the full 
deflection of the galvanometer is produced by .00006 ampere, a cur- 
rent which 625 volts would send through a resistance of over ten 
megohms ; while a current suflBcient to give a readable deflection 
would flow, under this pressure, through 3,000 megohms. With the 
arrangement shown, the maximum pressure which may produce 
leakage through the galvanometer is 6 volts. 

The main dial has a set of compensating coils, r^, for keeping 
constant the resistance between the sliding contact and the o end 
of this dial. By arranging the values of r,, r„ and the standard cell 
coils so that the resultant resistance beyond the 125 end of the dial 
is 300 ohms, the total resistance in the storage battery circuit being 

11737—07 8 



288 Bulletin of the Bureau of Standards. \vol 4, Ab. *. 

2,800 ohms, the point of maximum resultant resistance to the 
galvanometer current will come at the setting 70, when r^ is 1,400 
ohms; the resistance at 75 will be the same as at 65, and so on. 
Hence compensating coils are used up to the point 70, and by the 
use of cross connections no additional coils are needed beyond this 
point. 

A double-pole double-throw switch is used to change from stand- 
ard cell to emf., and a push button is provided in the galvanometer 
circuit. This button operates a double successive contact key 
having a protective resistance of 50,000 ohms in the first contact- 
The fine adjustment rheostat consists of two semicircular coils of 
insulated wire, the insulation being removed on the face to allow 
the sliding brush to make contact 

While the lowest range provided is nominally o to 125 volts, the 
range o to 5 volts may be had by using as the — emf. terminal the 
lever of the range switch, and adding sufficient resistance to the 
galvanometer circuit to make the proper total. In other words, 
the normal range of the potentiometer is from o to -5 volts, readable 
to .0004 volt (one-tenth of a scale division of the galvanometer). 
This range may be increased as desired by adding resistance in the 
emf. circuit at the rate of 100 ohms per volt. The reason for not 
making the lower ranges immediately available by setting the range 
switch is the danger of accident to these low ranges, due to the 
inadvertent application of the usual working pressures of 100 volts 
and over. The lower ranges are not frequently required, and may 
be arranged for specially as above described. It is proposed to con- 
struct an external rheostat which may be quickly connected up to 
give the ranges o to 12.5, o to 25, and o to 62.5 volts, the proper 
compensating resistances being thrown into the galvanometer cir- 
cuit for each range. The presence of this special accessory appa- 
ratus would constitute an indication of the need for caution as to the 
value of the voltage to be applied. 

A view of the instrument is shown in Fig. 6, from which it will 
be seen that the galvanometer is built into the rubber top, making 
the apparatus self-contained with the exception of the cells. The 
scale of the galvanometer is shown in Fig. 7. It has two sets of 
figures ; an upper -^th o in the center, and a lower with 5 in the 
center. Ten divisions of this scale correspond to one volt, the 






V ""' "■^.' 



Brooks.] A Deflection Potentiometer, 289 

upper set of figures being used when the dial reading ends in o, 
the lower set when ft ends in 5. Thus, if the dial reads no and 
the galvanometer needle stands at 22 divisions to the right, the 
emf. to be measured is 110+2,2 = 112.2 volts. In practice, the 
dial reading is mentally set at the center of the galvanometer 
scale, using upper or lower figures as required, when the value 
of the voltage can be read off from the scale, reading directly to 
tenths of a volt and estimating hundredths. The above applies to 
the first or principal range ; when the range switch is at x 2 or 
X 5 the operation of the instrument is exactly the same, but the 
values are to be multiplied by 2 or 5, giving a maximum range of 
625 volts. Should it be necessary to extend this by using a multi- 




Fig. 7. — Galvanometer scale, 

plier, this may be done with an error less than o;2 per cent of the 
deflection portion of the reading. At full scale deflection this is 
about .05 division, or about the limit of setting the needle on a line. 
Hence, in this design, multipliers introduce a negligible error. 

This instrument was built by The Leeds & Northrup Company, 
of Philadelphia, Pa., the galvanometer being supplied by the Weston 
Electrical Instrument Company, of Newark, N. J. It is so rapid 
and dead-beat in operation that the only limit to the rapidity of 
testing voltmeters with it is the ability of the operator to control 
the voltage and read the voltmeter under test The appliances now 
in use at the Bureau for voltage control will be replaced soon by 
others which will give the maximum speed of working. 



290 Bulletin of the Bureau of Standards. \voi. 4. no. 7. 

While intended primarily for direct current testing, the new 
instrument will be of assistance in testing alternating current volt- 
meters. This is done by the use of a transfer instrument which is 
equally correct on direct and alternating current ; the transfer instru- 
ment, the potentiometer, and the voltmeter to be tested being con- 
nected in parallel with each other, first on alternating, then on 
direct emf. The change from alternating to direct voltage is 
accomplished by a quick-acting snap switch, the circuit being broken 
for so short a time that the deflection of the transfer instrument is 
maintained. This results in a saving of time and the avoidance of 
zero errors, and is a very accurate and convenient method. 

Tests of this potentiometer in comparison with a five-dial standard 
potentiometer showed very small errors ; the result (using the 1 25 
volt range) being correct to within .01 to .02 volt when the deflec- 
tion of the galvanometer is small, and within .04 volt at the points 
of greatest error. For the higher ranges, and for the 5-volt range, 
the relative errors are equally small. This result will be improved 
by making a more accurate scale for the galvanometer, as some of 
the lines of the present scale are out of place by 0.2 scale division. 

5. SOURCES OF ERROR. 

The error in a measurement with the deflection potentiometer is 
the algebraic sum of two distinct errors. The first is due to the 
error of adjustment of the coils constituting the potentiometer, con- 
sidered as a null instrument, and affects the result when the galva- 
nometer deflection is zero, as well as for any value of the deflection. 
This error is present in standard potentiometers of every form; but 
the accuracy possible in the adjustment of resistance coils is such 
that it can be made negligibly small in comparison with the second, 
namely, the error in the value of jdB^ as given by the deflection of 
the galvanometer. The coils in the 2r circuit may not be correctly 
adjusted ; the fine rheostat in the battery circuit cannot be perfectly 
compensated for all settings on the main dial ; the scale of the gal- 
vanometer may be imperfectly graduated, and changes of temper- 
ature may afFect the reading of the galvanometer. It is therefore 
necessary to investigate these points, in order to keep these errors 
small and be able to allow for them when necessar>% Errors in the 
adjustment of the coils may be determined at any time by careful 



BrvoAs.] A Deflection Potentiometer, 291 

resistance measurements. If the error in the relative values of the 
coils in the main dial and of the volt box is such that corrections 
for the potentiometer as a null instrument are appreciable, a table of 
corrections can be made for the settings on the main dial. These 
corrections will then apply, whether the galvanometer is deflected 
or not. The accuracy required in the adjustment of the coils in 
the galvanometer circuit is much less than for the main dial and 
volt box coils, and errors due to this cause should be inappreciable, 
with good workmanship. 

It is necessary to investigate the error in the deflection reading, due 
to the fact that the fine rheostat in plan 5 makes the resultant resist- 
ance of r, and r, no longer a constant. This error will be greatest 
when the main dial setting is a maximum and the coarse rheostat 
r, a minimum. To reduce the error we may let one-half the total 
resistance in the fine rheostat take the place of an equal amount 
in the coarse rheostat r^; that is, one-half the fine rheostat may be 
considered part of the r^ for which the values of r^ are determined. 
Thus the fine rheostat will affect the resultant resistance one-half as 
much as would otherwise be the case. We have, then, the greatest 
error, in the present instrument, when r8= 297.5 ^^^ r,= 6,814. In 
the middle position of the fine rheostat 5.5 ohms is added to Tj, and 
the (normal) resultant resistance is 

303x6814 , 

^— *^-r>o— ^ = 290.1 ohms. 
303+6814 ^ 

Now let the remaining half of the fine rheostat be put in circuit, 
increasing r, to 308.5 ohms. The resultant resistance becomes 



308.5x6814 , 

o . ^0 —^ = 295.14 ohms. 
.^o8..s+68i4 ^^ ^ 



308.5+6814 

For maximum setting of the dial, for the above values of r,, the 
resistance in the galvanometer circuit between the contact point on 
the potentiometer wire and the zero end of the dial will be 

(390.1+9.9) 2500 ^367.86 ohms, 

290.1+9.9+2500 ' 

^H95d4±94i50o^^ ^ ^^ 
295.14+9.9+2500 



292 Bulletin of the Bureau of Standards, \yoi, 4, ^o. 9. 

the difFerence, 4 ohms, entering the total of 2,(xx> ohms in the 2r 
circuit, and requiring a compensation of 4 ohms. For the maxi- 
mum value of r, the compensation ^required is 3.45 ohms, to be 
added or subtracted for the two extreme positions of the fine 
rheostat. The mean of these was taken, and the compensating 
rheostat made 2x3.75 ohms. The error for this extreme position 

of the fine rheostat, if not comi)ensated, will be — — of the deflec- 

tion, or .06 scale division, which is about the limit of setting on a 
line. If this were the only source of error to be considered, it 
might be neglected; but it is desirable to avoid the accumulation pf 
small errors, and by proper arrangement of circuits it is easy to 
arrange for compensation. It is evident that if we compensate for 
the error which enters at the maximum setting of the main dial, we 
introduce the full error at the zero position of the main dial, and a 
proportionally decreasing error as the dial setting increases to a 
maximum. This is not objectionable, however, for on low readings 
of an instrument under test the accuracy is necessarily low, and the 
greatest accuracy is desired at or near full scale deflection. 

The method of combining the fine rheostat and the compensating 
rheostat in one simple dial may be seen diagrammatically in Fig. 5. 
It will be seen that the contact resistance of the lower end of the 
slider does not enter into the resistance of the wire AB, and the 
contact resistance of the upper end is in the galvanometer circuit 
It is possible to put the fine rheostat in other places, but it is 
believed that this plan is the simplest and most satisfactory. 

Errors due to imperfect graduation of the galvanometer scale 
depend upon the care taken by the maker, and may be determined by 
testing the galvanometer as an ammeter. The corrections to the 
deflection reading may be found for the galvanometer with its cir- 
cuit by the following plan. The storage cell is removed, and the 
terminals to which it had been connected are joined by a wire of 
negligible resistance. This reduces to zero the first term in the 
numerator of equation (17), and the deflection is now proportional to 
E; in other words, this makes E and JE identical. The value of 
E may now be adjusted to give suitable values of the deflection, E 
being measured by a standard potentiometer or calibrated voltmeter 
of suitable range. This method is necessary in plans 2, 3, and 4, 



BrooAs,] A Deflection Potentiometer, 293 

where a zero setting on the main dial is impossible. For plans i 
and 5 the storage cell may be in position and the main dial set at 
zero. 

Inasmuch as the 2,000 ohms of 2r contains, in the present design, 
576 ohms of copper in the galvanometer, the deflection part of the 
reading will var>' with the temperature. The galvanometer was 
found by trial to have practically zero temperature coefficient when 
used as an ammeter, the opposite coefficients of magnet and springs 
being sensibly equal. Hence the temperature coefficient of the gal- 
vanometer in use in the potentiometer is numerically that of the 

resistance of the 2r circuit, or -^^ x .0038 = .001 1 i)er degree C. 

' 2000 ^ J- & 

Hence, for 10° C above or below that at which the instrument is 
adjusted, the error will be i.i per cent of the deflection, and for 
maximum deflection of 2.5 volts the error would be 0.03 volt. The 
simplest way to care for this is to have a table giving values of 
JE corresponding to various readings, at different temperatures. 
Another plan would be to have a resistance dial marked in degrees, 
so that 2r might be maintained at the correct value, for any tem- 
perature. A third plan would be to use the device known as the 
Bristol compensator, in which the rise and fall of mercury in a tube 
varies the length of a platinum wire in circuit. This could be made 
of such proportions as to just compensate for the effect of the varia- 
tions in the galvanometer resistance. It is probable, however, that 
the first plan above is the best as well as the simplest, if all things 
are considered. For when the most accurate work is done, the tem- 
perature is usually kept near the standard, and as the galvanometer 
scale is not perfect, corrections will be required for the imperfec- 
tions, if not for temperature. Hence if corrections are to be made 
at all, they may as well include those for temperature. For most 
purposes, even in the laboratory, the correction for temperature can 
be neglected. 

It is important to note that in many applications of the deflection 
potentiometer the error of the result is almost independent of the 
error in the deflection part of the reading. For example, in testing 
a voltmeter the points checked are almost always a multiple of 5 or 
10, so that the galvanometer reading is quite small, unless the volt- 
meter is considerably in error. The reading of the galvanometer 



294 Bulletin of the Bureau of Standards. \voi. /, no, m, 

is the correction to the voltmeter at the given point, and may be so 
read off, using the + and — signs marked on the galvanometer 
scale. Thus the error in the galvanometer deflection is a fraction of 
a per cent of the small correction to the voltmeter, and is negligible. 
In using a deflection potentiometer to determine a definite voltage, as 
I GO or 1 20 volts, in order to mark the blank scale of an instrument, 
the method is a null one, and the result is independent of errors in 
the deflection part of the apparatus. 

A point that should be investigated, in a proposed design, is the 
accuracy with which the current from the storage battery can be 
adjusted, in terms of the standard cell. While this depends partly 
upon the available number of steps in the fine rheostat, it also 
depends upon the galvanometer sensibility and the value of the 
total resistance in the circuit containing the standard cell and the 
galvanometer. In the present design the drop for the standard cell 
is taken from 510 ohms, which is shunted by 2,290 ohms, giving a 
resultant resistance of 417 ohms. To this must be added 576 ohms 
galvanometer resistance and 160 ohms internal resistance of the 
Weston standard cell, giving a total of 1,153 ohms. If the current 
through the potentiometer wire is to be standardized in terms of the 
standard cell, to within one part in 10,000, then this fraction of the 
emf. of the cell, or .0001 volt, must give a noticeable deflection of 
the galvanometer. This emf. will send .0001 -^ 1,153, approxi- 
mately I X io~^ ampere through this resistance, and the resulting 
deflection will be one-twentieth of a scale division, which is about 
the limit, but can be observed when the needle is over, or close to, 
a line. If greater accuracy of the standard current were desired, 
using this galvanometer, it could be secured by using two or more 
standard cells in series, and taking the drop from a greater portion 
of the potentiometer wire. This would double or treble the value 
of the* small unbalanced emf. corresponding to a given error in the 
current, without increasing the resistance in the same proportion. 
An accuracy of one in 10,000 is, however, sufficient for all purposes 
for which this form of instrument would be used. 

It has been asked whether an error would arise if there is consid- 
erable resistance in the source of the unknown emf. to be measured. 
This question arises because the denominator of the expression for 
the gal vanometer current— ^nations (6) and (17) — contains the term 



Brooks.] A Deflection Potentiometer, 295 

R ^^-Tt—) ^^ resultant resistance of — paralleled by the remainder 

of R, To test this point we may assume a resistance r, in the 
source of E (page 231 of former article), when equations (i), (2), (3), 
and (4) remain unchanged, and (5) becomes 

^■.(^^^-+^)+^;|=^+^>. 

which reduces to the form previously given, namely : 

i,Rt^+uj=E (5) 

In this case, as before, E is taken to mean the potential difference 
at the terminals of the resistance R^ which is the value it is desired 
to measure. The value of t^ is thus unchanged, and the accuracy of 
the reading is independent of whether there is or is not resistance 
in the source of the pressure to be measured. The addition of resist- 
ance in the source would (theoretically) slightly afiFect the damping 
of the galvanometer, but in a practical case this effect would be inap- 
preciable. 

It is of interest to determine the magnitude of the error arising 
from the use of an external multiplier to extend the range. This 
error is, of course, zero when no current flows through the galva- 
nometer, but is present when such a current flows. In equation (5) 
let E increase to -£"', and let R be increased by the addition of an 
external multiplier R^. Then the equation becomes 

i^tzlj^i^^^iji'^E^^E+i^' 
P P 

which reduces to the original form of equation (5). 

R ^— T 

Considering the currents at the junction of — and R^—r-- we have 

h-U-ig=o (2) 

From equations (2) and (5) we get 



*. 


'R' 


y 


9 




E 
~R' 


I 

7" 





296 Bulletin of the Bureau of Standards, \voi. 4, no. 2. 

Further, 

When no current flows through the galvanometer this reduces 
to the ordinary formula for the use of an external multiplier, 



E' 



=^(i+f) (a7) 



Hence, when the galvanometer current is not equal to zero, and 

the ordinary factor 1+-0 is applied to the reading of the instrument 

to determine the emf. to be measured, the relative error c is given 
by the formula 

R^ Je 
___ p^r' E 

R 

"{-LrXR+R'YpE ^^ 

It is desirable to express the small quantity ^e (which is to be 
distinguished from ^E) in terms of -£*, as follows: 

_ J>s-E 

P 
^JE 

" P 



Equation (28) thus becomes 

RR' JE 



(29) 



Brooks.] A Deflection Potentiometer. 297 

The reason for this correction term is simply that when the resist- 
ance — is shunted by a larger value than the normal amount, 

R -^"7 , namely, by R ^^ — f- R'^ the resultant resistance is in- 

P P 

creased, and if the galvanometer gave a correct indication before, it 

will now give too small a deflection. This can be taken care of 

by applying the correction formula (29), or we may arrive at the 

same result by calculating the increment to 2r, and increasing JE 

in the same ratio. Thus, if R is increased by an amount R' 



which reduces to the form 

Hence the relative error in 2r is 

J (Lr) RR' 






2r -(^r){R-\-R')p* 
and the relative error in the observed value of the unknown emf. is 

^2r JE 



RR' ^E 

\l.r){R-\-R')f E 



(30) 



In equation (26), if a positive value of Je corresponds to an excess 

E 

of the potentiometer setting over —, or to values of E lower than 

that for which the galvanometer current is zero, E' will be lower 

R' 
than E {i-\- -^). When E is higher than the value for which the 
R 

galvanometer current is zero, the correction term in (26) becomes 

J?' 
positive, and E' is greater than -£* (1+ ^). 



298 Bulletin of the Bureau of Standards, \voi. 4. No. a. 

6. OUTLINB OF METHOD OF DESIGN. 

In designing a deflection potentiometer, the central and determin- 
ing feature is the galvanometer. From the current / for one scale 
division, the number of divisions m it is to give per volt of JE^ and 
the total resistance for critical damping, which latter is substituted 
as 2r, we may determine an approximate value of p from equation 
(11), namely: 

^''=/^ °''^=(2;5^ (11) 

As the resistance for critical damping is not sharply defined, we 

may modify the result somewhat, to give / a convenient integral 

value. From this tentative value of/ and the maximum emf. which 

it is desired to measure, we may find the fall of potential on AB, 

E 
which is — . For plan 5 this should be approximately a multiple of 

1.7 volts, and will show how many storage cells will be required. 
Having fixed the value of/, determine 2r by substitution in equa- 
tion (11). Deduct 5 or 10 per cent from 2r for a calibrating coil, 
and from the remainder deduct the resistance of tlie galvanometer. 

The rest of 2r is to be divided between R ^^l-and the resistance 

through the potentiometer proper, including the compensating resist- 
ance r^. This latter makes the resistance through the potentiometer 
(from the point of contact on the wire AB to the point A) constant 
and equal to one-fourth of the total equivalent resistance of the cir- 
cuit supplied by the storage cells. As the emf. of these cells, when 
freshly charged, will be about 2.1 volts each as a maximum, this 

2 I 
total equivalent resistance will be approximately -^r^, where r^ 

is the resistance of the wire AB; hence the constant resistance 

2 I 
through the potentiometer will be approximately z-o^'w ^^ ^ ^^^^ 

0.0 

approximation, divide the rest of 2r equally between this and if-cT"— , 

and determine the values of r«, and R. It is desirable, for adjusting 
and checking, that each step of r^ have an even and usual value of 



Brooks.} A Deflection Potentiometer. 299 

resistance, as 20, 50, or 100 ohms; with this in view, r^ may be 
chosen and R modified to suit. R may then be given an even value, 
the difference being taken up in the calibrating coil. It is desirable 
to m§ke R large, to reduce energy loss and consequent heating of 
the volt box coils; it is also desirable to make r„ large, as the drain 
on the storage cells is thereby reduced, and slight variations in 
rheostat contacts do not then exert as much influence on the 
current strength. 

The number of steps of the main dial is determined by two 
considerations. The smaller each step, the more accurate the 
instrument, because less of the total quantity is read by deflection. 
To go too far in this direction increases the size and cost of the 
instrument for a given range, and reduces the convenience and 
speed of working. The minimum number of steps is determined 
by the range of the galvanometer, assuming that emfs. are to be 
measured continuously from the lowest to the highest. 

The mechanical design should conform to good practice in such 
matters as reliable dial contacts, subdivision of coils in the volt box 
to reduce the dielectric stress per coil, and sufficient area in these 
coils to keep the heating small. The guard box around these coils 
is an essential feature, particularly when the instrument is to be 
used in damp weather. The grouping of the parts of the apparatus 
should be made with a view to rapidity and convenience of working, 
and will depend upon the judgment of the designer. 

7. CONCLUSION. 

In this and in the preceding article stress has been laid upon the 
desirability of using a pivoted portable form of galvanometer. This 
has been done because the aim has been to produce instruments that 
can be quickly and conveniently operated and moved from one place 
to another without requiring the special setting up which is neces- 
sary with reflecting galvanometers having delicate suspensions and 
small clearance between coil and pole pieces. Any galvanometer 
can be used which has a good zero and a constant that is reasonably 
permanent. It is desirable, if a reflecting galvanometer is to be 
used, to employ a taut suspension above and below, heavy enough 
to give quick working and good zero. For a given set of conditions 
the sensibility required can be determined, and the suspensions can 



3cx> Bulletin of the Bureau of Standards, Woi. 4. no. 2, 

then be chosen to give this sensibility. The matter of critical 
damping should be taken into account, as before mentioned. 

In the case of a deflection potentiometer for current measurements 
in connection with suitable shunts, which might have say 150 
millivolts as the upper limit of its range, the small amount of power 
available imposes much greater requirements upon the galvanometer 
than in the case of an instrument for the measurement of voltage, 
such as the one above described. The design of such a potentiometer 
for current measurements has been begun. 

While the potentiometer for voltage measurements, as described 
in this article, is best adapted to laboratory use, where voltmeters 
of various ranges must be tested, a simpler and less expensive instru- 
ment would answer all requirements in central station work. For 
example, a range of 105 to 125 volts, with provision to double and 
quintuple the range, would cover the most important requirements 
of the light and power station. The sensibility in this case would 
not need to be as great as for the laboratory instrument, so that a less 
sensitive galvanometer would be satisfactory. Preliminary work on 
the design of such an instrument has been begun. 

Washington, October 11, 1907. 



THE SELF AND MUTUAL INDUCTANCES OF LINEAR 
CONDUCTORS. 



By Edward B. Rosa. 



Formulae for the self and mutual inductances of straight wires 
and rectangles are to be found in various books and papers, but 
their demonstrations are usually omitted and often the approximate 
formulae are given as though they were exact. I have thought that 
a discussion of these formulae, with the derivation of a number of 
new expressions, would be of interest, and that illustrations of the 
formulae, with some examples, would be of service in making such 
numerical calculations as are often made in scientific and technical 
work. 

I have derived the formulae in the simplest possible manner, using 
the law of Biot and Savart in the differential form instead of Neu- 
mann's equation, as it gives a better physical view of the various 
problems considered. This law has not, of course, been experi- 
mentally verified for unclosed circuits; but the self-inductance of an 
unclosed circuit means simply its self-inductance as a part of a 
closed circuit, the total inductance of which can not be determined 
until the entire circuit is specified. In this sense the use of the law 
of Biot and Savart to obtain the self-inductance of an unclosed cir- 
cuit is perfectly legitimate. I have also shown how, by the use of 
certain arithmetical mean distances in addition to geometrical mean 
distances, the accuracy of some of the formulae can be increased. 

In the following demonstrations the magnetic field is assumed to 
be instantaneous ; in other words, the dimensions of the circuit are 
asstmied to be small enough and the frequency of the current slow 

301 



302 



Bulletin of the Bureau of Standards. 



\Vol.4.No.2. 



enough so that it is not necessary to take account of the finite 
velocity of propagation of the field. This may be done even when 
the field is integrated to infinity, as the distant magnetic field is 
canceled when two or more open circuits are combined into a closed 
circuit.' 

1. SELF-INDUCTANCE OF A STRAIGHT CYLINDRICAL WIRE. 

Let AB be a length / of a cylindrical wire of radius p traversed 
by current i distributed uniformly over the cross section of the wire. 





B 


dri> 


t 


\ 


^ 


p 


1 
1 
1 I 

1 I 

U 


_L 







c 



Fig. 1. 



The magnetic force at P normal to the paper due to an element of 
the cylinder of length dy is, 



'dy . ^ tady 

It is easy to show " that the force at any point outside a right 
cylinder is the same as though the current were concentrated at the 

^ For a discussion of the self-inductance of an open circuit closed by displacement 
currents in which the finite velocity of the field is taken into account see a recent 
paper by K. Ogura and C. P. Steinmetz, Phys. Rev., 25, p. 184, Sept, 1907. 

' Minchin, London Electrician, Sept. 27, 1895. 

M. Wien, Wied. Annal. 58, p. 928, 1894, gives a number of formulae for the self 
and mutual inductance of linear conductors. 



dN='^'' 



Roia.\ Inductance of Linear Conductors. 303 

axis of the wire. The force at P due to the whole length of the 
cylinder carrying unit current is then, 

fj_{'__ady_ _ l-b b 

Jo h*+(j-m^ -a^a'+{l-dy^a^a'~+b' ^'^ 

The number of lines of magnetic force aW, within the strip CD, 
of breadth dx, is found by integrating the expression for // along 
the strip. 
Thus, 

— ft ^~^ _ * "L 

The whole number of lines of force JV outside the wire which will 
collapse upon the wire when the current ceases is found by inte- 
grating aW with respect to x from x = ptox=cc . Thus, replacing 
a by ;r in (2), 

N= 2 fl^'- ^y- - 2 p.^+?-.- / log^-±V^] \,a) 
or, N= 2[/log .^+ V^+P^ V7«+^p«+p] (3) 

Lf^ = 2l\ log 1 approximately (4) 

This is the number of lines of force outside the wire due to unit 

current in the wire, and is therefore that part of its self-inductance 

L^ due to the external field. We must now find Z, due to the field 

within the wire. 

The strength of field at the point P within 

2ix 
the wire is — % • The number of lines of force 
P 

in the length / within the element dx is, 
therefore, J 

,^, 2tlxdx 

dN= a — 

P 

"737-07 9 




Fig. 2. 



304 Bulletin of the Bureau of Standards. \ voi. 4, No. 2. 

If we integrate this expression from o to p we have the whole 
number of lines of force within the conductor. Therefore 

li C 

//=-. I 2xdx=lz 



Iz C 



Thus there are t lines or tubes per unit of length within any cylin- 
diical conductor carrying a current /, or one tube per cm for unit 
current.^ 

The lines within the conductor do not cut the whole cross section 
of the conductor, as do those without. We must weight them, in 
estimating their effect on the self-inductance, in proportion to the 
area of the section of the conductor cut by each elementary tube. 

Thus, 

orA=i (6) 

Thus the / lines or tubes within the conductor contribute only half 
as much toward the self-inductance of the conductor as an equal 
number of lines outside the conductor would do. 

If the permeability of the wire is fi the part of the self-inductance 
due to the internal field is 

^=7 (7) 

We may derive (6) otherwise thus: The field at P is 

rr 2ix 

^= ?- 
The total energy W inside the wire is 



■kj"'""' 



V 

i 



'For convenience we may, however, speak as though there were many lines or 
tubes within the conductor due to unit current. 



jfosa] Inductance of Linear Conductors. 305 

where the integration is taken throughout the entire volume of the 
cylindrical wire. 

Thus, since dv^zirxldx 



But since W—-L^^ we have 

as found above by the first method (6). 

The total self-inductance of the length I of straight wire is there- 
fore the sum of L^ and Z,, as given by (3) and (6), or 



(9) 



z={/,c«'-±-V;'±f-V?+,-+^+,] 

= 2/ log ^ approximately. (10) 

= 2/[log^^-I + ^] (IX) 

where the permeability of the wire is /a, and that of the medium out- 
side is unity. This formula was originally given by Neumann. For 
a straight cylindrical tube of infinitesimal thickness, or for alternating 
currents of great frequency, when there is no magnetic field within 
the wire, we have for the self-inductance instead of (10) or (11) 

Z:=2/^log— — I (11/2) 

2. THE MUTUAL INDUCTANCE OF TWO PARALLEL WIRES. 

The mutual inductance of two parallel wires of length /, radius />, 
and distance apart rf will be the number of lines of force due to unit 
current in one which cut the other when the current disappears. 
This will be the value of N given by (2a) when the limits of inte- 
gration are d and 00 instead of p and 00 as before . 



3o6 

Thus 



Bulletin of the Bureau of Standards. [ voi. 4. No. 2. 



M=Il log ^tV^+^-*~V^^ + «^«+ J (12) 

= 2/ log -7 — 1 + 7 approximately (13) 

when the length / is great in comparison with d. 

Equation (12), which is an exact expression w^hen 
the wires have no appreciable cross section, is not an 
exact expression for the mutual inductance of two 
parallel cylindrical wires, but is not appreciably in 
error even when the section is large and d is small if 
/ is great compared with d. The force in that case 
due to A at all points outside A is exactly the same 
as though the current were concentrated at the center 
Oj of A; and the geometrical mean distance from Oj to 
the cross section of B is exactly the distance d between 
Oi and Og. The mean distance from Oj to all the 
points in the section of B is not, however, quite the 
same as dy although the mean of the log of these 

distances is log d. Hence there is a very slight difference in the 

last term of (12) depending upon the section of the wires and a still 

smaller difference in the 

other terms. (See p. 331.) 

This is, however, too small 

to be appreciable in any 

ordinary case, being a small 

quantity of the second order 

when / is large compared 

with d. 

3. THE SELF-INDUCTANCE OF A RETURN CIRCUIT. 

If we have a return circuit of two parallel wires each of length / 
(the current flowing in opposite direction in the tw^o wires) the self- 
inductance of the circuit will be, neglecting the effect of the end 
connections shown by dotted lines, Fig. 3, 



c rf > 


^-'>'—- b 



Fig. 3. 





Fig. 4. 



L=2L^-'2M 



j?«a.i Inductance of Linear Conductors, 307 

where L^ is the self-indnctance of either wire taken by itself, and yf 
is their mutnal inductance. Substituting the approximate values of 
Z, and J/ we have 



L = dX log- + - I approximately 



(14) 



The same result follows if we integrate the expression for the mag- 
netic force between the wires due to unit current, H— z/x. 
Thus, 



f 



N=l\ ?^ = 2/loR^ 



Multiplying this by two (for both wires) and adding the term due 
to the magnetic field within the wires we have the result given by 
(14). If the end effect is large, as when the wires are relatively far 
apart, use the expression for the self -inductance of a rectangle 
below (24); or, better, add to the value of (14) the self-inductance of 
AB+CD using equation (10) in which /=2AB. 

4. MUTUAL INDUCTAirCE OF TWO PARALLEL WIRES BY NEUMAinV'S 

FORMULA. 

Neumann's formula for the mutual inductance of any two cir- 
cuits is 

^^Jl^cosc^ (X5) 



In this case €=0 and cos €=i, r—Jd^-\-{y—b)^^ and the integra- 
tion is along both lines. 



M= 



The quantity in the brackets is the mutual inductance of the line 
AB and unit length of CD at a point distant b from the lower end, 
Fig. 4a. Now making b variable and calling it j, and integrating 
along CD from o to /, we have 



3o8 




Bulletin of the Bureau of Standards. 



[Vol. 4, No. t. 



Fig. 4a. 



M=Al\ogi 



^-^— V/'+^'+ 



"] 



which is the same expression (12) found 
by the other method. That process is 
more direct and simpler to carr>' out than 
to use Neumann's formula. 



5. MUTUAL mDUCTANCE OF TWO LINEAR CON- 
DUCTORS IN THE SAME STRAIGHT LINE 



We have found the self-inductance of the 
finite linear conductor AB by integrating 
the magnetic force due to unit current in 
AB over the area ABB'A', extending to 
the right to infinity, equations (3) and (9). 

In the same way we may find the 
mutual inductance of the conductors AB 




Fig. 5. 

and BC, lying in the same straight line, by integrating over the 
area S, (extending to infinity) the force due to unit current in AB. 



jpoia.i Inductance of Linear Conductors, 309 

The*magnetic force at the point P (of coordinates x^ y^ origin at 
A) due to current i in AB is 

The whole number of lines of force N^ included in the area S, is 

= ifv^''+ (/+w/- V^N^- v^+^ 



.JT 



+'-'-^±^#^' 






or il/^^ =/log-'^+/« log -^~, approximately. (17) 

This approximation is very close indeed so long as 7n does not 
approach infinity and the radius of the conductor BC (which we 
we have assumed zero) is very small. 

M=. 2/ log, 2 = 2/x 0.69315 cm. 
If w= 1000 /, (17) gives 

J/= / log, lOOI + ICHX) / log, i.ooi (18) 

= /log, 1001 + / approximately. 



3IO Bulletin of the Bureau of Standards. \ voi. 4. a'o. 2. 

If I— I cm, (18) gives 

M—\q%^ iooi + iooo log, I.OOI 

= 6.909+0.999=7.908. 

The self inductance of the short wire AB, suppose i cm long and 
of I mm radius, is 

A= 2(log —- .75) = 2(2.9957-.75) = 4.49i5 cm, 

which is a little more than one-half of the mutual inductance of AB 
and BC, BC being 1000 times the length of AB. 

In closed circuits, all the magnetic lines due to a circuit are 
effective in producing self-inductance, and hence the self-inductance 
is always greater than the mutual inductance of that circuit with 
any other, assuming one turn in each. But with open circuits, as 
in this case, we may have a mutual inductance between two con- 
ductors greater than the self-inductance of one of them. 

8B00in> DBRIYATION OP FORMULA (17). 

We may derive formula (17) for the mutual inductance of two 
linear conductors forming parts of the same straight line by use of 
formula (10). Let Li be the self-inductance of AB, Z,^ of BC, and 
L that of the whole line ABC. Then we have by (10) 

A=2/(logl^-3) 

Z=2(/+^)[log^-|] (19) 

The mutual inductance M^^ of the two straight lines AB and 
BC is then given by the expression 

log ~ ~ 2/log-y 

.-. 2J/,„=2(/+m)[^log^]+2/log^ 
or Mi„ = nog-^^ +'«log-^- 



Jfosa.] 



Inductance of Linear Conductors. 



311 



Fig. 6. 



which is equation (17), found independently above by integrating 
over the area Sj the magnetic flux due to unit current in AB. 

6. DEFINITION OF SELF-INDUCTANCE OF AN OPEN CIRCUIT. 

It is of course impossible to maintain a steady current in a 
finite straight conductor, or even to start a current ^ 

in such a conductor without having a return in 
the form of a displacement current. One can 
excite an oscillatory current in such a conductor, 
but the displacement current which doses the cir- 
cuit will produce magnetic force at a distance, 
and hence the actual self-inductance of such a cir- 
cuit is not the value of the self-inductance given by 
equation (9). 

The latter is the self-inductance of a part of a closed circuit due to 
the current in itself. The actual self-inductance of any closed cir- 
cuit of which it is a part will be the sum of the self-inductances of 
all the parts, plus the sum of the mutual inductances of each one 
of the component parts on all the other parts. Thus the self- 
inductance of a rectangle is the sum of the self-inductances of the 
four sides (by equation 10) plus the sum of the mutual inductances 

of I and 3 on each other, 
and of 2 and 4 on each 
other (taking account of 
sign the mutual induct- 
ances will be negative). 
Since the lines of force due 
to side I in collapsing do 
not cut 2 and 4, the mutual 
inductance of i and 3 on 2 
and 4 is zero. 

In a recent number of the 
Elektrotechnische Zeit- 
schrift,* Wagner shows 
that the total magnetic 



.^?^- 



--B' 



i 



Fig.7. 



flux of a finite straight conductor as derived from the Biot-Savart 
law has an infinite value, and concludes that the self-induct- 
ance is therefore infinite and hence that one can properly 



*Karl WUly Wagner, Elek. Zeit., July 4, 1907, p. 673. 



'312 



Bulletin of the Bureau of Standards, \voi. /, No. * 



speak of the self-inductance only for closed circuits. In reach- 
ing this conclusion he takes the integral expression given by 
Sumec * for the flux through a rectangle of length y and breadth 
x^'-x^ due to a finite straight wire of length /, as shown in Fig. 7. 
He then lets the rectangle expand, Xy^ being constant, and the ratio 
y\x^ remaining constant until x^ and y are both infinite. This gives 
an infinite value to the flux, but does not prove the self-inductance 
of the finite wire AB to be infinite, defining the self-inductance as I 
have done above. When the current in the wire decreases, the field 
everywhere decreases in intensity, and we think of the lines as collaps- 
ing upon the wire; that is, moving in from all sides upon the wire. 
But those lines above BB' and below AA' do not cut the wire, and 
hence contribute nothing to the self-inductance. For no lines of 
force cut across the lines BB' and A A' (BB' and A A' of course 
extend to infinity) as the field becomes weaker; the lines above BB' 
and below A A' collapse upon the axis cxte7ided of the wire AB. 

i 




rig. 8. 
Looking at it in another way, suppose the wire is divided into 
two parts at C, and the field between BB' and AA' is divided into 
Fj and F,. The lines of force in F, are due to the whole wire AB 
and not to AC simply, but in collapsing when the current ceases 
they cut only AC. So the lines in F, are due to the whole wire AB, 
but they cut only CB. Therefore in getting an expression for the 
self-inductance of the wire AB we must find the number of lines of 



*J. K. Sumec, Elek. Zeit.; Dec. 20, 1906, p. 1175. 



jfosa,] Inductance of Linear Conductors. 313 

force included between BB' and AA' integrating to infinity, and this 
is a finite number, as shown above, (3) or (4). 

To repeat what has already been said above, the self-inductance 
of a finite straight wire means its self-inductance as a part of some 
closed circuit. The infinite field at a distance due to it is canceled 
by that due to the other parts of the closed circuit which are not 
specified. We take account only of those lines which cut the given 
conductor in calculating its own self-inductance, and of those lines 
only which cut other parts of the circuit in calculating mutual 
inductances, ignoring the lines which do neither. 

In the case of an oscillating current in a finite straight wire, at 
the moment when the current i is a maximum and the potential of 

the wire is sensibly uniform and equal to zero the energy is -Li^^t 

where L is the self-inductance and i is thq current at the instant. 

The value of L is not the value given by (9) nor yet the infinite 
value found by Wagner, but is a finite value due to the finite con- 
ductor taken in connection with the return displacement circuit. It 
is indeed the self-inductance of a closed circuit, and not simply of 
the conductor in question. This I take it is what Wagner means, 
and not that we cau not speak of the self-inductance of an unclosed 
circuit in the sense in which it is done throughout this article. 

7. THE SELF-nn>UCTANCE OF A STRAIGHT RECTANGULAR BAR. 

The self-inductance of a straight bar of rectangular section is, to 
within the accuracy of the 'approximate formula (13), the s^me as 
the mutual inductance of two parallel straight filaments of the same 
length separated by a distance equal to the geometrical mean distance 
of the cross section of the bar. Thus, 

Z,= 2/|log^-i+yJ (20) 

where R is the geometric mean distance of the cross section of the 
rod or bar. If the section is a square, J? =.447 a^ a being the side 
of the square. If the section is a rectangle, the value of R is given 
by Maxwell's formula. (E. and M., § 692.) For example, when 
the rectangular section is 4X i cm, ^=1.118 cm. Thus the self- 



3^4 



Bulletin of the Bureau of Standards. 



\Vol.4.No.2. 



inductance of a straight square rod is a little less than that of a 
round rod of the same diameter, equal indeed to the self-inductance 
of a round rod of diameter 1.15 times the side of the square. 

Sumec has called attention to the fact that the geometrical mean 
distance for the area of a rectangle is very nearly proportional 
to the length of the two sides of the rectangle. Putting a and fi 
for the lengths of the two sides of the rectangle, and R for the 
geometrical mean distance of the rectangle from itself, 

^ = 0.2235 {a-\-^ nearly y&r all values of a and )8. 

The following table shows how nearly 

, for rectangles of 




Fig. 9. 



constant is the ratio 
different proportions : 

TABLE I. 



a+/3 



a and /? are the Length and Breadth of the Rectangles. R is the 
Geometrical Mean Distance of its Area. 



Ratio 


R 


R 


1 : 1 


0.44705a 


0.22353 


1.25: 1 


0.40235a 


0.22353 


1.5 : 1 


0.37258a 


0.22355 


2 : 1 


0.33540a 


0.22360 


4 : 1 


0.27961a 


0.22369 


10 : 1 


0.24596a 


0.22360 


20 : 1 


0.23463a 


0.22346 


1 : 


0.22315a 


0.22315 



The simple relation between the g. m. d. of a rectangle and the 
sum of its two sides, a+)3, is rather remarkable and, in view of 
the complicated formula employed in calculating R for a rectangle, 
very fortunate. Substituting this value of R in formula (20) we 

have, since log, - = 1.500 nearly. 



J!osa.] 



Inductance of Linear Conductors, 



315 
(21) 



as the formula for the self-inductance of a straight bar or wire of 
length / and having a rectangular section of length a and breadth )8. 
Substituting /=iocx), and a-\-fi=2 for a square bar locx) cm long 
and I square cm section we have, neglecting the small last term, 



Z=2000 



h-^+g 



2 2_ 

= 2000 (6.908+0.5) = 14816 cm 

= 14.816 microhenrys. 

This would also be the self-inductance for any section having a+yS 
= 2 cm. 
For a rectangular bar of section 1x4 cm, we have similarly 

2000 i" 

= 12.983 microhenrys. 
For a wire of rectangular section 1x4 mm, and 10 meters long 
Z= 17.588 microhenrys. 
8. TWO PARALLEL BARS.-SELF AND MUTUAL INDUCTANCE. 

The mutual inductance of two parallel straight, square, or rectan- 
gular bars is equal to the mutual inductance of two parallel wires 



r 2000 , i"i 

.= 2000 log, — — h- 



* — «..__> 




Rg. 10. 



3i6 Bulletin of the Bureau of Standards, \voi. 4. No. 2. 

or filaments of the same length and at a distance apart equal to the 
geometrical mean distance of the two areas from one another. This 
is very nearly equal in the case of square sections to the distance 
between their centers for all distances, the g. m. d. being a very little 
greater for parallel squares, and a very little less for diagonal squares* 
(Fig. 10). We should, therefore, use equation (13) with ^/ equal to 
the g. m. d. of the sections from one another; that is, substantially, 
to the distances between the centers. For the two parallel square 
rods 10 meters long and i cm square (Fig. 10) we have therefore 
for the mutual inductance using (13), and taking R = 2.o cm,^ 

M— 2000 (log, — i) 

= 2000(6.9077 — 1) 

1= 1 1.8 1 5 microhenrys. 

The self-inductance of a return circuit of two such parallel bars 
is equal to twice the self-inductance of one minus twice their mutual 
inductance. That is, 

Z = 2(A-^) 

= 2(14.812 — 11.815) 

= 5.994 microhenrys. 

If they were adjacent to one another the self-inductance of the two 
bars would be (their mutual inductance in that case being 13.190) 

21=2(14.812-13.190) 

= 3.244 microhenrys. 

These calculations are of course all based on the assumption of a 
uniform distribution of current through the cross section of the con- 
ductors. For alternating currents in which the current density is 
greater near the surface the self-inductance is less but the mutual 
inductance is substantially unchanged. 

•Rosa, this Bulletin, 8, p. i. 

^ Its more exact value is 2.0010, this Bulletin, 8, p. 9. 



Ifosa.} 



Inductance of Linear Conductors, 



317 



9. SELF-INDUCTAK CB OF A SQUAfiS. 

The self-inductance of a square may be derived from the expres- 
sion for the self and mutual inductance of finite straight wires from 
the consideration that the self-in- ^ 
ductance of the square is the sum 
of the self-inductances of the four 
sides minus the mutual induct- 
ances. That is, 

the mutual inductance of two 

mutually perpendicular sides being 

zero. Substituting a for / and d ^ 

in formulae (9) and (12) we have Fig. 11. 




Neglecting f>*/^', 

Zi— J/=2^ log 



2a 



•75+ /^+f] 



/KH-V2) 

Z=4(A-^) = 8a riog?-log,i±3/?+^- 
V 9 2 a 



-0.3358 



or Z,=8a(log- + ^—0.524) 



a 



!](22) 
(22^) 



where a is the length of one side of the square and p is the radius 
of the wire. If we put /= d^a — whole length of wire in the square, 



Z=2/(log /+4^-i.9io) 

or, Z= 2 /( log — 1. 910), approximately. 
9 



(23) 



31 8 Bulletin of the Bureau of Standards. [yoi. 4, no, 2. 

Formulae (22) and (23) were first given by Kirchholf • in 1864. 
If tf = icx) cm, p—o,\ cm, we have from (22) 

L—^00 (loge 1000—0.524) 
= 5107 cm = 5. 107 microhenrys. 
If /:)=.05 cm, 

^=5662 cm = 5.662 microhenrys. 

That is, the self inductance of such a rectangle of round wire is 
about 1 1 per cent greater for a wire i mm in diameter than for one 
2 mm in diameter. 

If l\p is constant, L is proportional to /. 

That is, if the thickness of the wire is proportional to the length 
of the wire in the square, the self-inductance of the square is propor- 
tional to its linear dimensions. 

If in the above case where p—o,\^ a =200 cm, 

Z=i6oo (log, 2000— 0.524) = 2x5.662 microhenrys. 

That is, for a square 200 cm on a side, Z is 1 1 per cent more than 
double its value for a square of 100 cm. on a side. 

10. SELF-INDUCTANCE OF A RECTANGLE. 

(a) The conductor having a circular section. 
The self-inductance of the rectangle of length a and breadth b is 

Z = 2(Z« + Z,-J/,-^,) 

where L^ and Z^ are the self-inductances of the two sides of length 
a and b taken alone. Ma and Af^ are the mutual inductances of the 
two opposite pairs of length a and ^, respectively. 

* G«sammelte Abhandlungen, p. 176. Pogg. Annal. 121, 1864. 



^osa.] Inductance of Linear Conductors, 

From (9) and (12) we therefore have, neglecting ^\c^^ 

z=4[<. lor 7-|''+<>]+4[* i<« f-l'+'l 



319 



Putting ^a*+^=rf, the diagonal of the rectangle, 
2ab 



^-' +^-f-*+p] 



or 



(24) 



L=A(a-^b)\o^^—a \og{a-\-d)—b log (-J+rf) 

For flr = 200 cm, *=ioo, p=o.i 

Z=8oi7.i cm = 8.01 7 microhenrys. 

(d) The conductor having a rectangular section. 

For a rectangle made up of a conductor of rectangular section, 
axA 



,= 2^ log-^+^+0.2235(a+^)J 




11737—07 10 



Fig. 12. 



320 Bulletin of the Bureau of Standards. [yoi, 4, Ai>. j. 



M^=2[a log £±^^- Va-rp^+3] 
and Z=2 {La^ Lf,— Ma— M^y as before. 

+ 0.2235 (a+/3)J 

+0.2235 (a+/9)6l 



Putting as before </=y a' +^'= diagonal of the rectangle, and assum- 
ing that the section of the rectangle is uniform; that is, that (a+/9)a 
= (a+i8)j, 

L=^ \{'^+b) log^-^r log(a+rf)-3 1og(*+flr) 

_^i + 2rf+o.447 («+/3)] (25) 

This is equivalent to Sumec's exact formula* {6a\ the logarithm 
of course being natural in (25), as elsewhere in this article. 
For a — b^2i square, 

Z=8a[log -?^^_^+^-log («+«V2)+o.2235 ^-^/^'\ 

Ifa=A 

Z=8a|log^+.447^+.o33j (25a) 

If a=iooo, a=i, 

Z,=8ooo [6.908+.033] 
= 8000x6.941 cm = 55.53 microhenrys. 



•Elek. Zeit., p. 1175, 1906. 



J^osa,] Inductance of Linear Conductors, 

For a circular section, of diameter i cm, p — o,^ 

I 



321 



Z=8ooo (log^j 2000- 



2000 



•524) 



= 8ooox 7.076 cm = 56.61 microhenrys, 

a little more than for a square section, as would be expected. 

11. MUTUAL INDUCTANCE OF TWO EQUAL PARALLEL RECTANGLES. 

For two equal parallel rectangles of sides a and b and distance 
apart d the mutual inductance is the sum of the several mutual 
inductances of parallel sides. Writing Mj^ for the mutual induc- 
tance of side I on 5, etc., we have 




Fig. 13. 




From (12) J/,,= 2 Vb log ^^^^^^WJ^^+d\ 

M„=. [* log '+^^P"- V?+*H^>+V?+5'] 
J/.= 2 [.r log ^±4±^"- V^^^^'+^J 

j/„=:2[.iog^v^_5Z±z:' 



^&'+d' 



V^'+^'+^'+V^+^'l 



322 



Bulletin of the Bureau of Standards. \yai. 4. No. * 






^ ^\b+4cf^b*^d* d )\ 



For a square, where a = d, we have 



(26) 



L ^V^+V2«"+^" ^ /J 



(27) 



These two formulae (26) and (27) may also be derived by inte- 
grating Neumann's formula around the rectangles. *• 

Formula (26) was first given by F. E. Neumann" in 1845. 

12. SELF AND MUTUAL nn>UCTANCE OF THIN TAPES. 

The self-inductance of a straight thin tape of length / and breadth 
b (and of negligible thickness) is equal to the mutual inductance of 
two parallel lines of distance apart R^ equal to the geometrical mean 
distance of the section, which is 0.22313 *, 



(1) 



(2) 



"^-— ft— > 



■^- (») 



h<r 



*b 



h<r- 



W 



(6) 



or logR = log*— ^ 

Thus, 

L=2l\ log ^ — I approximately 

= 2/[log^' + ^] (28) 



Fig. 14. 



For two such tapes in the same plane, coming together at their edges 

"Webster, Electricity and Magnetism, p. 45^. WaUentin, Theoretische Elektri- 

zitatslehre, p. 344. Fleming, . 

" AUgemeine Gesetze der Inducirten Strome, Abh. Berlin Akad. 



jfosa.] Inductance of Linear Conductors, 323 

without making electrical contact, the mutual inductance is 

J/=2/ log^-i 

= 2/[log ^'-0.8863] ^^^^ 

where R, is the geometrical mean distance of one tape from the 
other, which in this case is 0.89252 b. For a return circuit made up 
of these two tapes the self-inductance is 

= 4'(log ^')= 4/ log. 4 (30) 

= 5.545 X length of one tape. 

Thus the self-inductance of such a circuit is independent of the 
width of the tapes. If the tapes are separated by the distance 
i, -ff,= 1.95653 b and Z= 8.685 '• 

If the two tapes are not in the same plane but parallel and at 
a distance apart d (4) Fig. 14, then the geometrical mean distance 
between the tapes is given by the formula. 

log ^=^ log rf+i (1-^ log (*»+rf')+2^ tan -»| -\ (31) 

Ifrf=*,(5)Fig.9, 

log^,=log3+|-| (32) 

For a single tape 

log 7?,= log 3-3 {2^:^) 

R IT 

Hence log f^—~ and for the case shown at (5) Fig. 14, 

L = 2^1 — 2 J/= 4/ log -^* 

= 4/|=27r/ (34) 



324 



Bulletin of the Bureau of Standards, [yo/. /. jvo. 2. 



In this case also the self-inductance of 27r cm per unit of length of 
the pair of thin strips is independent of their width so long as the 
distance apart is equal to their width. The self-inductance is as 
much -greater in this case than in the case shown in (2) Fig. 14, as 

- is greater than log, 4, or 1.13 times. 
2 

13. CASE OF TWO PARALLEL PLATES.— NONINDUCTIVE SHUNTS. 

If a thin sheet of manganin or other conductor is doubled on itself 
to form a noninductive shunt we can calculate approximately its 
self-inductance bv the above method. 





rig. 15. 



By (31) 



Let 7=30 cm 

a =10 cm 

d= I cm 

log i?,= 1.0787 

log /^i = log, 10—^ = 0.8026 



Z = 4/(log ^,— log ^i) = i2ox 0.2761 

= 33.13 cm 
= .0331 microhenry's. 

If the resistance of the shunt is .001 ohm, and the 
frequency of the current through it is 100 cycles 



/^ = tan<^. 



.02 



and <^, the angle of lag of the current in the shunt behind the emf. 
at the terminals is approximately i? If « = ioc)0, <^=I2° nearly. 
By bringing the two halves of the sheet nearer together <f> could of 
course be reduced considerably below i ° for 100 cycles. This would 
be desirable for high frequencies. If the sheet were used straight 
in the above example the inductance would be six times as great, 
unless a return conductor were near. 



/^osa] Inductance of Linear Conductors, 325 

14. USE OF THE GEOMETRIC MEAN DISTANCE. 

In the approximate formula for the mutual inductance of two 
parallel wires 



M—2l\ log ——I 



we have only one variable, d. In applying this to determine the 
self-inductance of a thin, straight strip we make use of the theorem 
that the self-inductance of a circuit is equal to the sum of all the 
mutual inductances of the component parts of the circuit; that is, 
the sum of the inductances of every element upon itself and every 

other element. If there are n elements each carrying — th of the 



-*-- 



itsk- 



Rg. 16. 

current, each of these «' component inductances will be multiplied 

by -, if the total current is unity. Hence we see that the value of 
n , 

the self-inductance is the average value of the w' separate mutual 

inductances. But each mutual inductance is 

J/= 2/ (log 2/- log d- 1) (35) 

and as the first and third terms are constant, we have only to find 
the average value of log d^ where d is the distance between every 
pair of points in the straight line of length b which is the section of 
the strip. Since 

\ log rfj+log flr,+ log rf^ =i log d^d^d^ d^ 

--^og^^d,d,d,.,.d^ 
= logi? 

we see that what Maxwell called the geometrical mean distance R 
of the line is the «*** root of the product of the n distances between 
all the various pairs of points in the line^ n being increased to 
infinity in determining the value of R. This shows why the term 
geometrical mean distance was chosen. 



326 Bulletin of the Bureau of Standards. ivoi, 4, No. 2. 

The more exact formula (12) for the mutual inductance of two 
straight parallel lines may be written 

M= 2 [/ log (/+#+^)-/ log flT- y/H^+^l (36) 

In getting the mean value of this expression for n pairs of points 
along the line b we must find not only the mean value of log rf, but 
also the mean value of d itself and of d*. The latter means will not 
be the same as the geometrical mean distance R, but are the arith- 
metical mean distance and the arithmetical mean square distance. 
In order, therefore, to obtain an accurate value of the self -inductance 
L for the strip we should determine these arithmetical mean dis- 
tances for the section of the strip. 

15. DETERMINATION OF THE ARITHMETICAL MEAN DISTANCES OP A LINE. 

Let AB be the line of length b^ and we first find the arithmetical 

mean distance Si of the point P (AP = ^) from all the points of the 

line. 

A £ gf B 

^ ^ ^ 

Fig. 17. 

This may be done by integration, but the a. m. d. from P to all 

b—c 
points in the line to the right of P is, obviously, , and to the left 

-. Hence for the whole line 
2 

bSi = (b^c)+ ~c=^ -+~ 

2 ^ ^2 2 2 

.-. ^.-1-^+^- (37) 

To find S„ the a. m. d. of all points of the line from the line, or the 
a. m. d. of the line from itself we must integrate S^ over the line. 
Thus, putting c=x^ 



ieoia.] Inductance of Linear Conductors. 327 

Thus while the geometrical mean distance of a line is 0.22313 times 
its length the arithmetical mean distance is one-third the length. 

To find the arithmetical mean square distance Sj' from the point 
P to the line we integrate as follows : 



bS^^ ^\x-cydx=~-^cb^+(^b 
Jo 3 



...5-.»=|-^*+^ (39) 

3 

That is, the arithmetical mean square distance from one end of a 
line to the line is b*j^. Also 

To find the a. m. s. d. S,' we integrate again, changing c to x^ 

If now in formula (36) above we make the proper substitutions 
of geometrical and arithmetical mean distances, we shall obtain a 
more accurate expression for the self-inductance of a thin strip. 
Since d is small compared with /, formula (36) is very nearly equal 
to 

L= 2[/ log (2/[l +~^])- / log d^ /-f^+^] (41) 

= 2/[l0g2/-l0grf-I-^,+^] 

For log d'pvLt log ^— "5 
** d^ put dV6 

" d put ^/3 



328 



Then 



Bulletin of the Bureau of Standards. lyoi. 4, av>. >. 



, ,r, 2l ,1 , b b* '[ 



(42) 



which is the self-inductance of a straight thin strip of length / and 
breadth b. 

This formula neglects only terms in ^*/^> ^^'^ ^s therefore quite 
accurate. The value previously found (equation 28) is the same 
except for the last two terms. Formula (28) is of course accurate 
enough for most cases; but it is interesting to see what the more 
accurate expression is when we make use of the arithmetical mean 
distances in getting the values of the terms neglected in the first 
approximation. 

16. SELF-mDUCTANCE OF A CIRCLE OF THIN STRIP. 

Let us apply the principle of geometrical and arithmetical mean 
distances to obtain the self-inductance of a circular band of radius a 
and width b. This is a short cylindrical current sheet, for which we 
have the formula of Rayleigh : 

Z=4-{log^;-^+3^1og^+j)] (43) 



<■ — - — > 


d . 


1 

i 

I 

1 















Fig. 18. 

Coffin's formula gives some additional terms in **/^ ^^^ higher 
powers, but when b is not more than one-fourth of a^ Rayleigh's 
formula is correct to within about one part in 100,000, and may 
therefore serve as a check on the method of geometrical and arith- 
metical mean distances. The mutual inductance of two parallel 



^««1 Inductance of Linear Conductors, 329 

circles of radius a anci distance apart d is, neglecting tenns in d^\a^ 
and higher powers, 

^=H(-+r&)"^"-(^+rS)] (44) 

which may be written 

J/=4^a[(i+-3^^.)log 8a - log ^-^-log d-2-{^ (45) 

In addition to the g. m. d. to be used in the second term and the 
arithmetical mean square distance in the first and last terms we have 
to know the mean value of a product of g. m. d. and a. m. s. d. in 
the third term; that is, a term of the fonn 

5.' log R, 

To get this we must integrate as follows: 

bS; log i?,= fV-r)' \og{x—c)dx= 

*'5,» log i?,= ? r%-;r)'log (b-x)dx-{-^- fV log xdx 
3Jo 3Jo 

6\ ^ X2) (47) 

.-. ^.•logi?.= ^(logd-^) (48) 

We may now substitute in (39) as follows: 

log d= log ^— ^ 

3rfMog^=^(log*-^) 



330 
This gives 



Bulletin of the Bureau of Standards. [Voi. 4, a'o- »- 



J* \ , 8a I , *• "1 , , 

2?)^°^-3-2+I^'J (49) 



:47ra II- 



which is Rayleigh's equation (43). This confinns the values of the 
quantities Sg" and Sg'logR, employed in deducing the equation 
(49) from the formula (44) for M for two parallel circles. 

17. ARITHMETICAL MEAN DISTANCES FOR A CIRCLE. 

The arithmetical mean distance of any point P on the circumfer- 
ence of a circle from the circle is found by integrating around the 
circumference. Thus, since PB = 2a cos 6 




'■-P' 



TraSi — I 2a cos 6 . 2ad6 -■ 4a* 



TT 



(50) 



Since the a. m. d. is the same for ever>' point 
of the circle we have also 



Fig. 19. 



s,= 



4a 

IT 



(51) 



For the arithmetical mean square distance we have 
waS,^— I 4^* cos*tf . 2ad0=2 ira' 



'■'-f} 



.: S,'=S,' = 2a' 
and -^S^—a-^ 2 . 



(52) 



That is, the square root of the arithmetical mean square distance 
of every point on a circumference of a circle from every other 
point is equal to the radius of the circle into tl:e square root of 2. 
For a point P outside or inside the circle we have, since 



Inductance of Linear Conductors, 
PB=a^+d*-\-2adQos0 

-aS^^^a I ''{a^+d*+2adcos0)d0='ira{d^+a^) 



...5^« = ^«+fl 




Fig. 20. 



For the entire area of the circle with respect to the point P 



ira 



S,'=d'+'- 



331 



(53) 



(54) 



If d=o^ S^= — , the value for the area of the circle with respect to 

the center of the circle. 

For the area of a circle with respect to 
itself, the a. m. s. d., S,* would be found by 
integrating /\/'/=ri*+r,'— 2 r^r, cos (tfg— ^1) 
twice over the area of the circle. 

This was done in effect by Wien" in get- 
ting his formula for the self-inductance of a 
circle, which is a little more accurate than 
the formula deduced by the use of geometrical 
mean distances only, when the geometrical mean distances are used 
for the arithmetical mean distances. 

These examples are sufficient to illustrate the differences in the 
values of the geometrical mean distances and the arithmetical mean 

"M. Wien: Wied. Annal. 58, p. 928, 1894. 




Kg. 21. 



2^2 Bulletin of the Bureau of Standards. [ voi. 4, No. 2. 

distances, and the use of the latter in the calculation of self and 
mutual inductances. 

18. CONCENTRIC CONDUCTORS. 

The self-inductance of a thin, straight tube of length /and radius 
a^ is, when a^\l is very small, 

A-2/|^log^^-iJ (55) 

The mutual inductance of such a tube on a conductor within it 
is equal to its self-inductance, since all the lines of force due to 
the outer tube cut through the inner when they collapse on the 
cessation of current. The self-inductance of the inner conductor, 
suppose a solid cylinder, is 

A = ./[log|-|] 

If the current goes through the latter and 
returns through the outer tube the self-induct- 
ance of the circuit is, 

Fig. 22. since il/ equals Z, 

.-. z=2/[iogf;+^] (56) 

This result can also be obtained by integrating the expression for 
the force outside a^ between the limits a^ and ^j, and adding the 
term (equation 6) for the field within ^j, there being no magnetic 
field outside «,. Thus 







as above. 



If the outer tube has a thickness a^—a^ and the current is distrib- 
uted uniformly over its cross section the self-inductance will be a 



/fosa] 



Inductance of Linear Conductors, 



333 



little greater, the geometrical mean distance from a^ to the tube, 
which is now more than a^ and less than «,, being given by the 
expression 

log«.=^-^^°^'?^y^^-"-'-^ (57) 

t*3 U^ * 

Putting this value of log a in (56) in place of 
log a^ we should have the self-inductance of 
the return circuit of Fig. 23. 

If the current is alternating and of very 
high frequency, the current would flow on the 
outer surface of a^ and on the inner surface 
of the tube, and L for the circuit would be 




Fig. 23. 



t 



f t 



P 



Rg. 24. 



Z,= 2/ log 



(58) 



19. MULTIPLE CONDUCTORS. 



If a current be divided equally between two 
wires of length /, radius p and distance d apart, 
the self-inductance of the divided conductor is the 
sum of their separate self-inductances plus twice 
their mutual inductance. 

Thus, when </// is small. 



or L 



= ^{i°? i^ji- i\= 4^°^ S)i~ "] ^^^^ 



where rg is the g. m. d. of the section of the wire = 
\d 0.7788^. 

If there are three straight conductors in paral- 
lel and distance d apart, as shown in Fig. 24, the 
self-inductance is similarly 



'=4^°^(^i-^] 



(60) 



334 



Bulletin of the Bureau of Standards, 



{Vol 4, ^'0.2. 



The expression (rgd*)i is the g. m. d. of the multiple conductor. 
For example, suppose in the last case /=iooo cm, p=2 mm, 
d= I cm. Then (rgd*)h = o.^^8 cm and 

y r 2000 "1 

Z=2000 log, 5 1 

L ^0.5380 J 

= 2ooox 7.221 cm = 14.442 microhenrys- 
If the whole current flowed through a single one of the three 
conductors the self -inductance would be 



Z=2000 



I log, -3 =17.92 microhenrys, 



or about 25 per cent more than when divided among the three. 

Guye has shown" how, by the principle of the geometrical mean 
distance, one can calculate very readily the self-inductance for any 
number of similar conductors in multiple when they are distributed 
in a circle, Fig. 25. 

If there are n conductors uniformly spaced on a circle the geo- 
metrical mean distance R of the system is given by 



1 ^__ ^^ log r, + n log (r„ , r,, r,„) 

= - (log ^i+log (r^j. r,3 r„i)) 



(61) 




Fig. 25. 

where r^ is the g. m. d. of a single conductor (=0.7788^, p being its 
radius) and r^ is the distance between centers of the conductors i 
and 2, etc. If a is the radius of the circle on which the conductors 
are distributed 

"C. E. Guye, Comptes Rendus, 118, p. 1329; 1894. 



/fasa.] Inductance of Linear Conductors, 335 

logi?=^log(r,«^"-0 

or R^(r^na^''j'' ^^^) 

The proof of this, as given by Guye, depends on the following 
theorem: 

If the circumference of a circle is divided into n equal parts by 
the points A, B, C, . . . and M be any point on the line through 
OA (inside or outside the circle), then putting OM=;r 

A?^— ^" = MA.MB . . . MN (Cotes's theorem). 
Dividing by MA = j:--^, 

x^-' + ax'"'^^ , . . . a'"' = MB ' MC . , . . MN 
Making M coincide with A, and hence x=^a^ 
na'^'^^AB ' AC . . . AN 

= «« ■ ^13 • • • • ^m 

which substituted in (61) gives (62). 

Since the self-inductance of a length / of the multiple system is 
equal to 

Z-2/[log^^-l] (63) 

we see that the calculation for any case is simple when ^, a^ and n 
are given. Thus, suppose a = 2 cm, ^ = 0.5 cm, and n = 6^ 

r^na""'^ ~ 0.3894 X 6 X 32 

•••^=(74765)* = 2.0525 

If the separate conductors have only half the diameter supposed, 
namely, ^=0.25, the g. m. d. R will be considerably less. In this 
case 

^ = (0.1947 X 192)*= 1.8285 cm. 
"737-07 II 



33(> 



Bulletin of the Bureau of Standards, 



[Vol, 4. J^'o. 2. 



Thus, in the first case, the self-inductance of the six parallel con- 
ductors is equal to that of a thin tube of radius 2.0525 cm, and in 
the second case to that of a tube of radius 1.8285 cm. As « 
increases and p decreases the value of R approaches 2 cm as a limit, 
the multiple conductors forming in the limit a tube of infinitesimal 
thickness, the value of R for which is its radius ^^, in this case 2 cm. 
If a larger conductor at the center carries the going current, and 
the return is by the multiple conductor, the mutual inductance of 
the larger upon the others is 




M—2l\ log 1 



(64) 



Fig. 26. 



where 



since the g. m. d. of the central conductor on 
each of the others is a. 

The self-inductance of the return system is 

L^ — 2l 



L^ — 2l 
M^2l 



log 2/— log {r^na^'-y' — 1 1 

^logi^-i] 

^ ...Z=2/riog^'-log(r,«a«-y"+^] (65) 

For a = 2 cm, ^^=1 cm, ^ = 0.5, « = 6, /=iooo cm 

i:=2CHX) log. 4 -log, (2.0525)+^ 
= 2000x0.9173 = 1.835 microhenr>-s. 

If the inner conductor were surrounded by a ver>' thin tube of 
radius 2 cm for a return, in place of the six wires, the self-inductance 
of the return circuit would be 

Z = 20oo[log|+^] (66) 

= 2000 X 0.9431 cm = 1 .886 microhenrys, 
a little greater than in the preceding case. 



Rosa.] 



Inductance of Linear Conductors, 



337 



If the central conductor is also a multiple system, Guye has 
shown " how to find the mutual inductance of the two when the 
arrangement is symmetrical, the g. m. d. of the two systems being 
derived by the aid of Cotes's theorem. In this case 



logi?„ = ilog«-V) 



n 



or^,, = «~^,«)» 



(67) 




Fig. 27. 

Thus, if «,= 2 cm, a^ — \ cm, and « = 6, 

i?=(64-i)*= 1.9947 

and as n increases R|, approaches 2 as a limit, as it would be for 
two concentric tubes of radii i and 2. Ri and R, for the two sepa- 
rate systems being given by (62) and R„ by (67), the self-inductance 
of a return circuit with one system for the going current and the 
other for the return is readily calculated, being 



^=^'"«|i^. 



(68) 



These examples are sufficient to illustrate the calculation of the 
self and mutual inductance of multiple circuits by the principle of 
the geometrical mean distance. 



338 Bulletin of the Bureau of Standards, \ voi 4, so, 2. 

20. SELF-INDUCTANCE OF A ''NONINDUCTIVE" WINDING OF SOUND WIKES. 

Suppose a to-and-fro winding of insulated wire in a plane, the 
length of each section being /, the distance apart of the adjacent 









Fig. 28. 

wires, center to center, being d^ and the wire of radius p. The 
resultant self-inductance of one of the wires is equal to the self- 
inductance of the wire taken by itself plus the mutual inductance 
of all the others upon it. The mutual inductance of wires 2, 2', 
4, 4', 6, 6', etc., upon wire A at the middle of the group tends to 
increase the self-inductance of A, while the mutual inductance of 
I, i', 3, 3', 5, 5', etc., tends to decrease the self-inductance of A. 
Hence, if L^ is the self-inductance of A by itself and M^ is the 
mutual inductance of wire i on A, etc., we have for Z^ the total 
resultant self-inductance of wire A of length / the following 
expression : 

Z^ = A + 2il/,-f2il/,+ 2il/,+ . . +2J/„_i-2J/,-2il/, 

— 2^1/5— 2^1/7— . . . —M,, 

+ (^M,^M,)+{Af,^A/,)+{Af,-Af,)+ (69) 

= 2/llog +n-2/log^-2/ log ^-2/ log-— 

+ 2/ log ^+2/ log 5+2/ log 7+ ... . 



Jiosa.] Inductance of Linear Conductors, 339 

(where 2« is the whole number of wires) 

= ^l\^o^U\-A~\ (7x) 

where the constant A depends on the whole number of wires. Since 

LJ 3^ 5_i7 (2«-l)(2«+l)_7r 
2« ' 4* ' 6« (2«)« " :"2 

when « is infinite," we see that equation (70) becomes for an infinite 
number of wires 

This formula (72) was first given by Mr. G. A. Campbell." He 
has recently communicated to me by letter his (unpublished) demon- 
stration, which is different from that given above and gives the 
value of L for an infinite number of wires and not for any finite 
number, which is the more important case. 

For 2n — 2^ A =0 

2« = 4,^ =log.2 =.6931 

2« = 6, -^ =log,- =.2876 

2«=IO,yi = log.-^ =.3522 

45 

2n = 14, ^ = ^^^* jf^ " '^^^ 

2n=iS,A = 2 log,— =.3961 

'*I/)ney's Trigonometry II, p. 155. 

"* Elect. World, 44, p. 728; 1904. There is an error in this formula as originally 
printed; it should have //2 for coefficient instead of /. 



340 



Bulletin of the Bureau of Standards. 



\VoL 4, ^'o. 2. 



2n = 38,A= =4253 

2n=7o,A= =4373 

TT 



2n = co,A = log,- 



:.45i6 



Thus we see that the resultant self-inductance of the middle wire 
of such a " noninductive '* system is always less than that of a sin- 
gle pair, by the quantity 2 A/. If the winding is such that d= 3/), 

log, - + - = 1-35) approximately, and the self-inductance of the mid- 

P 4 
die wire is about two-thirds as much when there is a great number 
of such wires side by side as when there is a single pair, and about 
three-fourths as much if there are 10 such wires (5 pairs). 
The self-inductance of the end wire will be more, being 



= 2/ 



L P 4. 



= 2/ 

= 2l 



i^§:?+ ']+(.I/-J/3)+(A/,-^,) + . 



-^^^^^J:^^)] 



log-+ ' 
L ^' 4 



-.,] 



where A^= —log, - for 2« = 4 

= — log.-Q^ '' 2«==6 etc. 

o 

For the next to the end wire 



Z = 2/[log^+l-^.] 



where A^ — log, - for 2« = 4 
o 

= log,- " 2« = 6, etc. 
For the second from end wire 
A^=log^ — for 2n=8 



/iosa.] Inductance of Linear Conductors. 341 

These examples show how the self-inductance of any particular 
wire of such a winding may be computed and the average or total 
value found. For a large number the average value of A would 
evidently not be far from 0.40. 

21. CASE OF NONUfDUCTIVE WINDING ON A CmCTTLAR CYLINDER. 

The self-inductance of a single circular turn would be approxi- 
mately 



A = 47rJ log -^-1.751 

where a is the radius of the circle and p is the radius of section of 
the wire. The mutual inductance M^ of two adjacent turns is 

My^ — AfirA log -, — 2 L approximately, 

where d is the distance between centers of the two turns. This 
approximation is close only so long as ^ is small compared with a. 

Similarly M^ = 47r J log — — 2 and hence 

^l/j — J/, = 47r<2(log 2) 
i]/,-J/,r=47r^log y ^ ^^^ 

= 47rd log + — 47rd log 2 — log^ + logS for 2« = 8tums 

= 4^^i[log^+^-^J (73) 

where A has the same values as in the case of parallel straight wires 
laid noninductively in a plane, provided the length of the coil is 
small compared with the radius, so that the approximate formula 



342 . Bulletift of the Biireati of Standards, \voi. 4, A-b. 2, 

for M is sufficiently exact. The values of A are positive except for 
the end wire and depend on the number of wires and the position 
of the particular wire in the winding. If the radius is not large in 
proportion to the length of the coil, the constant A is a little less 
than for the wires in a plane. It is to be noted that the self- 
inductance of such a winding does not depend on the size of the 

wire, but on the ratio , so that if a fine wire has a proportionally 

P 
close spacing its self-inductance is the same. For a given pitch the 
self-inductance is of course greater as the wire is finer. 

Taking A for the entire spool as approximately equal to 0.40 
formula (73) becomes 

Z = 2/ log - — o. 1 5 approximately (74) 

where L is the self-inductance of a " noninductive " winding in a 
plane or on a cylinder of any radius, / being the total length of the 
wire, p is radius and d the mean distance between adjacent turns, 
center to center. In practice d p can not be obtained with great pre- 
cision, so that an accurate value of the constant A is not necessar}% 
Moreover, the precise value of L for such a winding is seldom or 
never required. 

A spool of 200 turns of wire with a = 1 cm, rf'p = 4,(taking A =0.4) 
would have a self-inductance of 

L=^wa (log, 4— 0.15) X 200 
= 8(X>7r (1.386— 0.15) 
= 3100 cm = 3. 1 microhenrys. 

Since deriving the above expressions Mr. Campbell has sent me an 
expression for the mean value of the constant A for a noninductive 
winding in a plane for any number of wires. His demonstration is 
as follows: 

Take 2« straight conductors, each of radius />, lying in a plane 
with adjacent wires at distance d center to center as before, the cur- 
rent traversing adjacent wires in opposite directions. We may 
regard this as a system of n circuits, each consisting of two adjacent 
wires. The total inductance will be equal to n times the self- 
inductance of one of the circuits plus 2 («— i) times the mutual 



Rosa.] Inducta7tce of Linear Conductors. 343 

inductance of two adjacent circuits plus plus 

two times the mutual inductance of extreme circuits. That is, 
per unit of length of the system: 

Z=;iUlog +1J+2 {n-^i) 2log^^+2(«-2) 2log3-:^H 

I —lor (^^^-3) (2^-1 ) 

^^•^'"'^(2;/— 2)(2//-2) 

or for a total length of wire / 



= 2l\] 



iogf+i-iogj+4-(;--) 



^o.5772±^^>- ^JJ approximately (76) 

The value of the constant A of formula (71) as calculated by Mr. 
Campbell for various numbers of pairs of wires are given in the fol- 
lowing table: 

TABLE I. 
The Constant A for Formula (71) 



n 


Value of A by 
Formula (75) 


n 


VftlueofAby 
PormuU (ts) 


1 


.000 


10 


.350 


2 


.144 


15 


.377 


3 


.213 


20 


.392 


4 


.255 


25 


.402 


S 


.283 


30 


.409 


6 


.304 


100 


.436 


7 


.319 


200 


.443 


8 


.332 


300 


.446 


9 


.342 


Infinity 


.452 



344 Bulletin of the Bureau of Standards. \vol 4, No. 2. 

As stated above, the constant A of formula (73) is very nearly the 
same as in (71), and hence the same values may be used for approx- 
imate calculations. 

The above results by no means exhaust the subject of the self and 
mutual inductance of linear conductors ; enough has been given, 
however, to serve in some measure as a guide in solving other cases 
arising in practice. 

Washington, September 15, 1907. 




~^z^4^ 




i^ik 



THE ATOMIC WEIGHT OF CHLORINE. 



By WOfiam A. Noyes and H. C. P. Weber. 



The ratio of the atomic weights of oxygen and chlorine is 
of extreme importance on account of the number of atomic 
weights based either directly or indirectly upon the atomic weight 
of chlorine. 

During the last few years alone, since the determination of the 
ratio of silver to chlorine by Richards and Wells/ the atomic 
weights of a considerable number of the common elements have 
been determined, basing them on the value of chlorine. These 
values have been calculated on the oxygen basis, assuming that 
the ratio silver : oxygen: 107.93: 16 is correct. Guye and Ter- 
Gazarian * have called attention to a possible source of error in 
the chlorate ratio of Stas, correction for which would bring the 
value of silver down to 107.89. The newly accepted value 14.01 
for nitrogen also points to the lower value of 107.89. Very nearly 
at the close of this work conclusive evidence has been presented 
by Richards and Forbes ' and by Richards and Jones * that the 
value 107.93 for silver is too high. The only direct comparison 
between hydrogen and chlorine which we have is that of Dixon 
and Edgar.* In this determination hydrogen was made to biuii 
in an excess of chlorine. The hydrogen was weighed absorbed 
in palladium and the chlorine in the liquid form in a glass bulb. 
The hydrogen and chlorine were caused to unite in a large globe 
of glass containing a small quantity of water to absorb the hydro- 

*J. Araer. Chem. Soc., 27, p. 459; 1905. 

^Compt. Rend., 148, p. 411. 

'J. Amer. Chem. Soc., 29, p. 808; 1907. 

Mbid., 29, p. 826; 1907. 

•Phil. Trans., Series A, 205, p. 169. Chem. News, 91, p. 263. The determina> 
tions of Deutsch (Dissertation, 1905), from the laboratory of Professor Guye, are 
scarcely of sufficient accuracy to be considered as atomic weight determinations. 

345 



346 Bulletin of the Bureau of Standards, [1^01.4,1^0,3. 

chloric acid formed. Corrections were applied for the quantity 
of chlorine remaining uncombined, by titrating the amotmt of 
iodine liberated by it from a solution of potassium iodide. A 
further correction was applied for the amoimt of chlorine used up 
in liberating oxygen from water, by determining the amount of 
oxygen set free. 

The fact that there was only one such direct determination of 
the ratio between chlorine and hydrogen, together with the oppor- 
tunity afforded of carrying out the determination with hydrogen 
prepared in the same apparatus used for generating the hydrogen 
in the recent determination of the ratio of hydrogen to oxygen, 
made a new determination seem to be worth while. 

The method we have used, besides being a direct comparison 
between hydrogen and chlorine, involves the principle of com- 
plete synthesis with the determination of the weights of all the 
substances reacting and of the reaction products formed. Briefly 
stated, the method consists in weighing the hydrogen absorbed 
in palladium and the chlorine in the form of potassium chloro- 
platinate. The hydrogen is passed over the heated potassium 
chloroplatinate, from which it removes chlorine to form hydro- 
chloric acid. The hydrochloric acid formed is condensed in a 
third section of the apparatus and weighed. We have thus the 
weight of hydrogen used, the weight of chlorine removed, and 
the weight of hydrochloric acid formed. In this manner two series 
of ratios, each independent of the other, are obtained. 

Working in this manner and with hydrogen prepared under 
the same conditions and at the same time as that used in the 
determination of the ratio of hydrogen to oxygen by one of us, we 
believe that we have very favorable conditions for bridging the 

gap. 

Ag-CloH-0 

PURIFICATION OF MATERIALS AlfD WEIGHING. 

Hydrogen. — ^The hydrogen used in these experiments was pre- 
pared and purified in the same manner as described in a previous 
paper on the atomic weight of hydrogen. • 

•Noyes, this Bulletin, 4, p. 179. 
J. Am. Chem. Soc., Dec., 1907. 



-JJ^ ] The Atomic Weight of Chlorine. 347 

The gas was taken from the generatmg apparatus at intervals 
covered by the period of the work on hydrogen. Consequently 
all remarks concerning its character and purity as used in the 
hydrogen-oxygen ratio apply to these determinations. As in that 
work so in this, two methods of generating the hydrogen were 
employed. In the last series of determinations the hydrogen was 
obtained by the electrolysis of a solution of barium hydroxide. 

Platinum. — The platinum used in the preparation of potassium 
chloroplatinate was originally obtained in the form of platinum 
sponge. The preliminary purification consisted in dissolving 
this in aqua regia and evaporating to remove nitric acid. The 
separation from other platinum metals was carried on according 
to the method of Schneider and Seubert, as described in Graham 
Otto's Lehrbuch.' 

The solution of chloroplatinic acid was boiled for half an hour 
with excess of caustic soda, acidified, and the platinum precipi- 
tated as potassium chloroplatinate. The chloroplatinate so 
obtained was reduced with sodium formate. The platinum black 
was then heated with dilute hydrochloric acid to remove iron and 
washed until it commenced to go through as colloidal platinum. 
It was then redissolved and the process repeatedly gone through 
imtil the mother liquors from the chloroplatinate precipitation 
were practically colorless and free from other platinum metals. 
As the same platinum was continually used, and imderwent a 
large number of successive solutions and reductions dtiring the 
preliminary work, it seems safe to assume that it was sufficiently 
pure. 

Potassium ChloropkUinaie, — During the preliminary work it was 
soon discovered that the preparation of chloroplatinic acid by the 
use of aqua regia was unsatisfactory. The removal of nitric acid 
by the process of repeated evaporation was tedious and, at best, 
uncertain. To overcome this difficulty and eliminate nitric acid 
entirely, a process of dissolving the platinum electrolytically in 
purified hydrochloric acid was devised. This proved quite satis- 
factory and will be described in the next paper. After solution of 
the platintun in hydrochloric acid had been effected the solution, 
which contained approximately 120 g of platinum and meastired 

^Graham Otto's Lehrbuch, 5th edition, 4, p. 1153. 



348 Bulletin of the Bureau of Standards, ivoi. 4, No. 3. 

500 cc, was evaporated to about one-half its volume in a glass-stop- 
pered wash bottle. At the same time a current of chlorine was 
passed through the boiling solution. The chlorine used for this 
purpose was prepared by the action of pure potassium permanga- 
nate upon chemically pure hydrochloric acid which had been pre- 
viously boiled with a small quantity of permanganate to instire its 
freedom from bromine compoimds. The solution of chloroplatinic 
acid thus obtained had a beautiful bright color, matching almost 
exactly that of ao.i per cent solution of methyl orange. It con- 
tained about 100 g of hydrochloric acid in excess and after filtration 
and dilution to i Hter was used directly for the precipitation of 
potassium chloroplatinate. For this purpose a solution of potas- 
sium chloride was prepared, using an excess of one-third above the 
theoretical quantity dissolved in i liter of water. The excess of 
potassium chloride as well as the excess of hydrochloric acid in the 
chloroplatinic acid were deemed necessary to check hydrolytic 
decomposition. For the same reason the precipitation of potas- 
sium chloroplatinate was carried out with as concentrated solutions 
as practicable. The precipitation itself was carried out by pouring 
the platinum solution into the potassium chloride in a fine stream, 
the precipitate meanwhile being agitated thoroughly by a ciurent 
of air. In some cases as much as four hours were spent in precipita- 
ting 300 g of potassium chloroplatinate. The potassium chloro- 
platinate so obtained was of a pale-yellow color, resembling precipi- 
tated sulphtir and was microcrystalline. It was filtered from the 
mother liquor by means of the suction pump, washed with water, 
and finally with alcohol and ether. After having been removed 
from the hardened filter it was heated for some time in a large plati- 
num dish on an electric air bath until the greater part of the mois- 
ttire retained had been driven off. The quantity necessary for one 
determination was then transferred to a hard glass tube. This 
tube was placed in a cylindrical air bath which could be raised to 
a temperature of 400®. The potassium chloroplatinate was grad- 
ually raised to this temperature, a current of air, dried successively 
by sulphuric acid and phosphorus pentoxide passing over it con- 
tinuously. The behavior of the salt under these conditions served 
as a criterion of its purity. At the exit of the current of air a wash 
bottle was placed with a drop of methyl orange. At first a small 



Nc 



^^r^ '^f^^ Atomic Weight of Chlorine. 349 

quantity of moisture and hydrochloric acid passed off. Finally, 
however, a point was reached where no further hydrochloric acid 
could be detected in the issuing air stream. At this point the 
heating was stopped, usually after the chloroplatinate had been 
heated to 400® for about 7 hoiu-s or more. It seems that the 
chloroplatinate, when ptu-e, will stand the temperature of 400° 
indefinitely, in a nonreducing atmosphere, without suffering any 
change chemically. No appreciable quantity of hydrochloric acid 
could be detected after the hydrochloric acid and water held 
mechanically had once been driven off. This all, provided the salt 
was pure to start with. In the first trials, in which the chloro- 
platinate had been prepared by the use of aqua regia, its behavior 
was entirely different. In these cases decomposition set in in the 
neighborhood of 250® and seemed to go on progressively through 
the whole mass of the salt. 

After having been dried in this manner the chloroplatinate was 
transferred to the final apparatus with little or no exposure to the 
air through an opening which was sealed off after filling. In this 
it was subjected to final drying at 350*^ and evacuation, as described 
under the manipulations. 

Potassium Chloride. — As a starting point for the preparation of 
pure potassium chloride the ptu-est commercial article obtainable 
was taken. This was first recrystallized from a solution made 
slightly alkaline with potassium hydroxide to remove traces of 
ammonia which were present. The salt was then redissolved in 
water and chlorine passed through the hot solution for several 
hours, after which it was concentrated and the potassium chloride 
allowed to crystallize out. Following this the salt was recrystal- 
lized five times from water, precipitated three times by alcohol, and 
finally precipitated from aqueous solution by purified hydrochloric 
acid gas. The crystals in these various processes were separated 
from the mother liquors by centrifugal drainage. 

This potassium chloride certainly contained less bromine than 
I in 50,000. To test for bromine the following process, a modifi- 
cation of that described by Andrews,* was adopted. The 
flask, A (Fig. 2), is fitted with a ground-glass joint at B, 
which ends in an extremely fine capillary at C. The side tube, D, 

® Jour. Am. Chetn. Soc., 29, p. 275; 1907. 



350 Bulletin of the Bureau of Standards, 1^01.4,^0.3. 

has a trap to prevent spray from being carried over. An ordinary 
distilling flask is affixed to the end of this side tube with a rubber 
stopper in such a manner as to bring the side tube well into the 
bulb of the flask E. The flask A is charged with 200 cc of dis- 
tilled water, 20 cc of ^ potassium iodate and 20 cc of 2 N nitric 
acid. The flask E contains about 5 cc of a 4 per cent solution of 
potassium iodide, which must not liberate iodine upon being 
acidified. The flasks are then connected by means of the stopper 
at F and vacuxun applied. The capillary tube which is groimd into 
the flask at B is connected with a carbon dioxide generator, and 
after vacuum has been applied should yield a fairly steady stream 
of bubbles through the liquid, so as to insure regular boiling and at 




Fig.2. 

the same time not appreciably to diminish the vacuum. It is 
desirable to have a pure neutral gas, such as carbon dioxide or 
nitrogen, passing through the capillary, since traces of reducing sub- 
stances in the air used would vitiate the results. The gas passing 
through the capillary, besides insuring regular boiling, acts as a 
diluent for the steam formed and as such checks the reaction : 

H,0 + Brg=2HBr+0 

The flask containing the potassium iodate and nitric acid mixture 
is then heated on the water bath until 100 cc have distilled into the 
flask containing the potassium iodide. If the resulting distillate 
is colored by the presence of free iodine, the process is repeated 
after adding water to make up for the quantity distilled off, until 



«vJi.] The Atomic Weight of Chlorine. 351 

a satisfactory blank is obtained. Then 3-5 g of the potassium 
chloride to be tested are dissolved in a little water and added to the 
flask containing the iodate and the volume of the solution made up 
to 250 cc again. The distillate containing the free iodine corre- 
sponding to the amount of bromine distilled over is then titrated 
with a solution of thiosulphate corresponding to i mg of bromine 
per cc. To 5 g of potassium chloride, which had been treated until 
blank distillates were obtained, the following quantities of bromine 
were added and f otmd : 

Added i.o 0.5 0.3 o.i mg 
Found 1.0 0.52 0.36 0.12 mg 
The potassium chloride used for precipitating potassium chloro- 
platinate contained less than o.i mg bromine in 5 g or 1:50,000. 
This amount it is safe to assume was further reduced in the 
preparation of potassium chloroplatinate. 

Hydrochloric Acid, — The hydrochloric acid used in the prepara- 
tion of ptu-e hydrochloric acid was free from sulphuric and nitric 
acids. It was treated by allowing chlorine to bubble through it 
for one day. Following this, air was bubbled through the acid 
saturated with chlorine until the chlorine was expelled and the 
acid was again colorless. Usually the air was left passing through 
the acid overnight, a reduction of about one-fifth in the volume 
of the acid, due to evaporation, taking place with the removal 
of the excess of chlorine. During the further manipulations in 
preparing chloroplatinic acid it was further subjected to action 
of chlorine twice, namely, dining electrolysis of the platinum and 
evaporation of the platinum solution. 

Chlorine. — All the chlorine used was generated by the action 
of pure potassium permanganate on hydrochloric acid which had 
been previously boiled with a small quantity of potassium per- 
manganate. 

Water, — ^The water used was obtained by redistilHng distilled 
water with alkaline permanganate, rejecting the first part of the 
distillate until it no longer contained ammonia. 

Balance and Weights, — The balance and weights were identical 
with those described under the atomic weight of hydrogen." The 

• Noyes, this Bulletin, 4, p. 179. 
J. Amer Chem. Soc., Dec, 1907. 



352 Bulletin of the Bureau af Standards, w&i. 4. N0.3. 

air of the balance case was dried by means of a current of air as 
described in the previous paper. Each piece of apparatus was 
weighed with a corresponding coimterpoise approaching it 
within I cc in volume and 30 g in weight. In the case of the 
hydrogen the counterpoise was within 0.3 cc of the voliune and 
2 g of the weight of the palladium tube. 

AU pieces were rinsed with distilled water after having been 
used in a determination. After having been wiped dry, they were 
suspended for some time in a desiccator through which a current 
of dry air was passing before being transferred to the drj'^ air of 
the balance. For the hydrogen apparatus 12 to 24 hours were 
allowed in order to attain constant siuface conditions. The 
current of air through the balance was stopped 15 to 20 minutes 
before a weighing was made. Duplicate weights were taken at 
intervals of an hour or more and rarely differed by more than 
0.05 mg. 

Weights, — The weights were calibrated to vacuum standard 
in the Biu*eau of Standards. The small correction necessary on 
account of the difference in volume between the brass and plat- 
inum weights was included in a table with the corrections for the 
errors of the weights. 

hethod of carrying out the determination. 

FIRST SERIES. 

There are three parts to the apparatus, which was prepared 
for a determination in the following way: 

The Palladium Tube, — ^This consisted of a cylindrical tube with 
a stopcock sealed on at each end. The tube at one end was bent 
downwards at right angles and draA/vii out to a tip at B. Con- 
nection with the hydrogen generator was made by sealing the 
tip into a corresponding socket with Khotinsky cement. The 
three-way stopcock at B was then opened in the position so that 
the small amount of air in the limb of B was swept out. Com- 
munication was then established between the palladium and the 
hydrogen generator and hydrogen was led in until no more was 
absorbed. The stopcock at A was then opened and the hydro- 
gen allowed to sweep through the apparatus for a short 
while. The stopcocks were then closed, and after cleaning the 



«*?;&.] ^^^ Atomic Weight of Chlorine, 353 

apparatus it was ready for weighing. Before the apparatus was 
used the*first time it was repeatedly charged with hydrogen and 
the hydrogen driven out at 400°. After that the tube was ready 
for charging anew at the end of each experiment. 

Chloroplatinate Tvbe, — This tube had the general form as shown 
in the accompanying photograph. The potassium chloroplatinate 
was introduced through the curved neck which was open at D. 
For this purpose the hard glass tube in which the chloroplatinate 
had been heated to 400° was connected to it by a short piece of 
stout rubber tubing, and the chloroplatinate was shaken into the 
apparatus. The end D was then sealed off without allowing 
vapors from the flame to enter the tube. After this was done 
the apparatus was attached to the Sprengel pump and evacuated 
to a few thousandths of a millimeter at a temperature of 350°. 
This temperature was maintained for about 4 hours. After clos- 
ing the stopcock, disconnecting and rinsing after it was cool, the 
apparatus was transferred to the desiccator before weighing. 

Absorption Tube for the Hydrochloric Acid. — This consisted of a 
bulb having a volume of about 100 cc. It terminated in two tubes 
with stopcocks and sockets to fit the tips of the two tubes from the 
platinum apparatus at E. Fifty cc of boiled distilled water were 
filled into this bulb. It was then evacuated by means of the 
Sprengel pump, which was protected by an extra phosphorus 
pentoxide tube in this case. The evacuation was continued as 
long as air could be removed from the apparatus or liquid. Usu- 
ally it was found necessary to allow the partly evacuated apparatus 
to stand for a day before the last traces of air could be removed 
from the water. After evacuation the apparatus was rinsed and 
set in the desiccator for weighing. After the different portions 
of the apparatus had been weighed they were set up as shown in 
the photograph. The potassium chloroplatinate and the palla- 
dium charged with hydrogen were each enclosed in an electric 
heater. These are lowered in the photograph to show the 
apparatus. 

The tip, B, of the hydrogen tube and C of the chloroplatinate tube 
were connected with each other and with the Sprengel pump by 
means of a T-tube. The two tips from the chloroplatinate tube 



354 Bulletin of the Bureau of Standards. \voi,4,no.3, 

were connected to the two corresponding sockets of the absorption 
tube. These joints were made with Khotinsky cement." 

The joints were perfectly tight and no leakage was ever discov- 
ered. After the three parts of the apparatus had thus been connected 
with each other and with the vacuum pump the connections were 
evacuated. The gas in the two connecting limbs at E was removed 
by opening the stopcocks at F and pumping the gases out over the 
chloroplatinate, which had meanwhile been brought to a tempera- 
ture of about 300°. When every part of the apparatus had been 
evacuated to a few thousandths of a millimeter, as shown by the 
McLeod gauge attached to the pump, connection with the pump 
was cut off. The stopcock of the hydrogen apparatus at B was 
then opened and gradual heating of the hydrogen tube commenced. 
Then the stopcock at C was opened very gradually and the hydro- 
gen admitted to the chloroplatinate. Next the four stopcocks 
communicating with the absorption tube were opened. This was 
done very gradually, to prevent a sudden rush of gas into the 
absorption tube and consequent carrying over of the finely divided 
potassium chloroplatinate. In doing this the stopcocks were 
opened in such order that communication was first established 
through the tube entering the chloroplatinate apparatus at the 
lower level. Following this, communication was established by 
means of the adjoining tube. The purpose of the double connec- 
tion between the chloroplatinate and the absorption tube was to 
prevent stagnation of the gas current between the two parts of the 
apparatus. A little hydrogen was always carried along with the 
hydrochloric acid toward the absorption apparatus. This would 
tend to accumulate and block the current. By making the level 
of the second tube somewhat higher than that of the first, the tend- 
dency of the hydrogen to rise would cause a direct and continuous 
flow. Actually, this arrangement proved entirely satisfactory. 

The apparatus remained in this condition for several hours. 
The temperature of the palladium tube generating the hydrogen 
was allowed to rise slowly at such a rate that the pressure in the 
apparatus was kept at or below one atmosphere. This pressure 

*<^P. G. Nutting, of this Bureau, has supplied us with a cement of this same char- 
acter, which seems to answer the purpose as well as the Khotinsky. It is made by 
fusing together equal parts by volume of rosin and pure rubber. 



^^ ] The Atomic Weight of Chlorine, 355 

was measiired by means of a small mercury manometer, M, which 
formed a part of the connecting T-tube, BC. The closed end of the 
manometer contained a little air. By this means it was possible 
to measure any pressure from zero to more than one atmosphere 
with a light manometer 8-10 cm in length. 

When it was deemed that a sufficient quantity of hydrogen 
had been evolved from the palladium tube, the stopcock, B, of 
this part of the apparatus was closed and the palladium allowed 
to cool off. The temperature of the tube containing the chloro- 
platinate was allowed to rise to 350°. At the same time the 
absorption tube, which had been cooled by ice during the earlier 
part of the experiment, was now cooled to— 20° by a mixture of ice 
and dilute sulphuric acid. The hydrogen remaining in the appa- 
ratus upon cutting off the palladium tube was continuously con- 
verted into hydrochloric acid and removed as such by the water. 
This could be followed by means of the manometer, M, previously 
mentioned. After two or three hours the manometer had reached 
the lowest point which it would indicate. At this point the stop- 
cocks, G, of the absorption tube were closed. The conditions 
prevailing at this moment were as follows: 

The chloroplatinate tube still contained an excess of potassium 
chloroplatinate and was at a temperature of 350°. 

The absorption tube was at a temperature of — 20°. The resid- 
ual pressure throughout the apparatus was very low. 

Under these conditions but a very minute quantity of hydro- 
gen could have escaped conversion into hydrochloric acid. To 
determine this, connection with the Sprengel pump was again 
established and that part of the apparatus between the stop- 
cock, B, of the palladium tube and the stopcocks, G, of the absorp- 
tion tube was evacuated to the best vacuum obtainable by the 
pump — usually a few thousandths of a mm. The gas pumped 
out was collected in a eudiometer and analyzed. In analyzing 
the gases their volumes were read at a pressure of about one-sixth 
to one-seventh of an atmosphere, making accurate determination 
possible. Thus the volume of i cc under these conditions repre- 
sented less than 0.02 mg of hydrogen. 



356 Bulletin of the Bureau of Standards. \voi. 4.^^0,3. 

The residtial gas having been pumped out of the apparatus, 

all stopcocks were closed and the apparatus taken apart. All 

traces of the cement adhering to the glass where the various 

pieces had been joined were carefully removed. The pieces were 

then rinsed with distilled water, when sufl&ciently cool, wiped 

dry, and transferred to the desiccator. The following day they 

were weighed. The determination itself required about 8 hours, 

of which about 2 hours were used for the evolution of hydrogen 

and about 3 hours^ for the pressure to drop from atmospheric to 

practical zero. 

SBCoim 8BRIB8. 

Before giving the results obtained by the first series it may be 
just as well to tirni to the manipulations giving the second set of 
values. They are essentially the same as in the first series with 
this difference: the hydrochloric acid generated was condensed as 
a solid by cooling with liquid air and connection with all other 
parts of the apparatus was cut off before it was absorbed by water. 
The point in view was this. During the period of absorption of 
the hydrochloric acid it might be possible that a transfer of water 
would take place from the absorption apparatus to the chloroplati- 
nate apparatus and remain there in spite of the fact that there was 
a difference of 370° in temperature between the two parts and a 
very high vacuum. This would cause the apparent amount of 
chlorine transferred to appear lower than the real. Or there was 
the possibility of the water vapor reacting with the material in the 
chloroplatinate tube. To eliminate these possibilities the reaction 
was so carried on that the chloroplatinate was at no part of the 
determination in contact with water vapor. 

Further, this series differs from the first in that the hydrogen 
used was generated from a solution of barium hydroxide, the 
hydrogen in the first series being obtained from a sulphuric acid 
electrolyte. The absorption apparatus in the second series (which 
simply took the place of the water absorption tube) was con- 
structed as follows: 

The bulb, K, was designed for the condensation of the hydro- 
chloric acid and had a volume of 100 cc. It terminated in a neck 
from which led two exit tubes provided with the stopcocks, H and 
I. The stopcock at I was provided with two perforations so that 



^^] The Atomic Weight of Chlorine. 357 

communication could be established either between the chloro- 
platinate tube and K, or between the two bulbs, K and L. The 
bulb, L, had a volume of 70 cc and contained the water for the 
absorption of the hydrochloric acid. At N a miniature mercury 
manometer was affixed. This was found absolutely necessary in 
order to follow the conditions of pressure during the transfer of the 
solid hydrochloric acid in K to the water in L. Indeed, previous 
to the attachment of this device to the apparatus every determina- 
tion was lost either by the bursting of the apparatus or the blowing 
out of the stopcocks. By making the air space above the mercury 
of capillary tubing, while the remainder was about 1.5 mm in 
bore, satisfactory readings could be obtained both at normal and 
reduced pressures and there was no danger of the mercury being 
sucked out of the manometer. 

To prepare the apparatus for weighing, somewhat more than 
50 g of water were filled into L through a small opening at P. 
The water was then boiled, and when all air had been expelled 
the opening at P was sealed off. The whole apparatus was then 
evacuated with the Sprengel pump, the last traces of air being 
removed from L by opening the stopcock I momentarily until 
the limit of the pump was reached. Rinsing, drying, and desic- 
cation then completed the preparations for weighing as usual. 
The apparatus was then put together and prepared for the deter- 
mination in precisely the same manner as in the first series with 
the one difference that the absorption apparatus. III A, was now 
connected at E instead of the absorption tube, III. Communi- 
cation with the water bulb, L, was entirely cut off during the first 
part of the determination. The condensation bulb, K, was 
plunged in liquid air at the beginning and kept at the tempera- 
ture of boiUng air throughout the determination. 

In opening the stopcocks to obtain communication between 
the various parts of the apparatus very great care had to be exer- 
cised, as the first rush of gases into the chilled condensation bulb 
often carried some finely divided chloroplatinate with it. In a 
few cases it was not possible to avoid this. Since this chloro- 
platinate remained in the condensation bulb, K, its amount 
could be found at the end of the determination and a suitable 
correction applied. 



358 Bulletin of the Bureau of Sta?idards, i voi. /. No. 3, 

After communication had been established between the hydro- 
gen tube, the chloroplatinate tube, and the condensation tube, 
the hydrogen tube was cautiously heated so as to obtain a con- 
stant and steady rise in temperature. Somewhat more care was 
necessary in this series, as there seemed to be a greater tendency 
for the pressure in the hydrogen apparatus to fall below that of 
the remaining parts. This would result in the finding of hydrogen 
chloride in the palladium tube at the end of the experiment. Suit- 
able corrections were made for this and will be spoken of with 
the other corrections. When the hydrogen tube had reached a 
temperature of from 150° to 160°, it was judged that the requi- 
site amount of hydrogen had been evolved. The stopcock from 
the hydrogen tube was then closed. Any temperature above 150® 
sufficed for the reduction of the chloroplatinate by the hydrogen, 
but at the end the temperature of the chloroplatinate tube was 
run up to 400°. The condensation bulb was kept fully submerged 
in liquid air. After the supply of hydrogen had been tmned oflF 
the pressure in the apparatus gradually sank until all hydrogen 
had been used up and all hydrochloric acid condensed. The con- 
ditions then were: Excess of the chloroplatinate at 350° to 400°; 
the hydrochloric acid at about —180°, and a very low residual 
pressure. The stopcocks of the condensation tube were then 
closed and the residual gases in the remaining parts of the 
apparatus pumped out. 

The condensation tube was then separated from the remaining 
parts of the apparatus and the transfer of the hydrochloric acid to 
the water commenced. The water bulb, L, was plunged into ice 
water and the condensation bulb, K, removed from direct contact 
with the liquid air but not entirely beyond the cold vapors. As 
soon as the pressure of the hydrochloric acid had risen to a small 
part of an atmosphere communication was established with the 
cold water in L. After some hydrochloric acid had been absorbed 
by the water the bulb, L, was cooled by ice and dilute sulphuric 
acid, instead of by ice alone. With the aid of occasional shaking 
of the absorption bulb the last of the condensed hydrochloric acid 
was finally absorbed by the water. With cautious manipulation 
the pressure in the apparatus did not rise above one-half atmos- 



«^i.] ^^'^ At079iic Weight of Chlorine. 359 

phere during the transfer and remained at a few millimeters at the 
close. The stopcock, I, between K and L was then closed, and 
the apparatus was cleaned, rinsed, wiped, and set aside to be 
weighed. The determinations of the second series required about 
ten hours from beginning to end. About two hours were con- 
sumed in transferring the solidified hydrochloric acid from the con- 
densation to the absorption bulb. The solidified hydrochloric acid 
resembled snow in appearance and the greater part of it was 
absorbed by the water without passing into the liquid state. 
Towards the end of the transfer, when the absorption became less 
rapid, the remaining hydrochloric acid would liquefy, attended by 
a sudden rise in pressure. Shaking of the absorption tube imme- 
diately reduced the pressure and caused the liquid hydrochloric 
acid to solidify to a glassy solid. 

ERRORS Aim CORRECTIONS. 

Hydrogen. — If there were any errors due to a contamination of 
the hydrogen, they are not apparent. The hydrogen was pre- 
pared and purified with all possible precautions. It was repeat- 
edly tested for impmities in the work on hydrogen and none or 
only negligible quantities found." 

Two corrections on the weight of hydrogen were foimd neces- 
sary. The first of these was the amount of hydrogen remaining 
in the chloroplatinate tube at the end of the determination and 
pumped out with the residual gases to be analyzed. In eight 
cases out of the twelve this correction was applied, the maximum 
being o.ii mg, the minimum 0.0 1 mg, and the average 0.047 mg. 
The determinations affected are i, 2, 4, 5, 6, 7, 11 and 12. The 
second correction was due to hydrochloric acid in the palladium 
tube. Under certain conditions, when the current of hydrogen 
from the palladium tube was not sufficiently rapid, hydrochloric 
acid found its way back into the palladium tube, either by diffu- 
sion or by being drawn back. Correction for this was readily 
applied. After having been weighed the hydrogen apparatus 
was charged for the succeeding determination. The tube was 

" Noyes, this Bulletin, 4, p. 179. 
J. Amer. Chem. Soc., 29, Dec, 1907. 
15298 — 08 2 



360 Bulletin of the Bureau of Standards. \voi, 4. J^o.3. 

fitted with a stopcock at both ends, as may be seen in the photo- 
graph. After the palladium had been saturated with hydrogen 
the stopcock farthest from the hydrogen generator was connected 
to a Liebig flask containing water colored by a drop of methyl 
orange. The stopcock at A was opened while the hydrogen 
generator was kept going and the hydrogen bubbled through this 
water before escaping. If the presence of hydrochloric acid made 
itself known, the palladitmi was heated to 160° to expel the larger 
part of the hydrogen it had absorbed and with it any hydrochloric 
acid present. It was then allowed to cool with a ciurent of hydro- 
gen passing through it and it was finally filled again at normal tem- 
peratures. The hydrochloric acid absorbed by the water was then 

N 
titrated by - - sodium or baritmi hydroxide. The real weight of 

the hydrogen was greater than the apparent loss of the tube by the 
weight of the hydrochloric acid found. This correction was 
applied in determinations i, 3, 4, 10 and 11, varying between 0.35 
and 9.26 mg and averaging 4.8 mg. 

Chlorine from the Loss of the Platinum Tube. — The purity of the 
chlorine entering into the composition of the chloroplatinate has 
been spoken of. The maximum amount of bromine in the ingre- 
dients used seems to have been i in 50,000. The resultant error 
in the weight would be half of this, since 35.5 g are replaced by 80, 
or 1 : 100,000. There seems to be ample justification for consider- 
ing this point beyond question. 

The only other impurities which could possibly affect the results 
were volatile products in the platinum or elements capable of pro- 
ducing volatile products, such as ammonia, water, hydroxyl, or 
oxygen. The method of preparation seems to preclude the possi- 
bility of the presence of ammonium salts. The potassium chloride 
was especially treated to free it from these. Following this there 
was repeated treatment with chlorine in hot solution. The final 
heating of the chloroplatinate to 400° over an extended period of 
time must have caused the destruction and removal of any ammo- 
nium compounds which had escaped previous treatment. 

The three following impurities, water, hydroxyl, or oxygen, in 
the platinum salt were somewhat more difficult of treatment. It 



^^^U.l ^^^ Atomic Weight of Chlorine. 361 

is known that potassium chloroplatinate hydrolyzes in aqueous 
solution. With this point in view the precipitation of potassium 
chloroplatinate was carried out in concentrated solutions with both 
an excess of potassium chloride and hydrochloric acid and the 
mother liquor was removed as soon as practicable. It was shown 
that by heating sufl&ciently long at 400^ all occluded hydrochloric 
acid could be removed, the chloroplatinate being perfectly neutral 
after this treatment. This served as indirect evidence that the 
water was also removed. The agreement between series i and 2 
may be considered as additional evidence on this point. In the 
first series the chloroplatinate had opportunity to become saturated 
with water vapor at the temperature of 350° during the course of 
the experiment. In the second series it was in equilibritun with 
solid hydrochloric acid at — 180? Now hydrochloric acid with its 
well known affinity for water vapor may be considered as a very 
perfect drying agent. Yet the difference between the two series 
is I in 10,000. One hundred and twenty grams of potassium 
chloroplatinate were used. The presence of 0.05 per cent moisture 
in this salt would have raised the atomic weight of chlorine found 
from 35.184 to 35-244- 

Further, in the second series it was noticed that if the condensa- 
tion tube for the hydrochloric acid was allowed to contain a trace 
of moisture before the determination was begtm this would remain 
as a trace of aqueous hydrochloric acid after the gas had been 
transferred from this part of the apparatus to the absorption bulb, 
the temperature during this transfer remaining, of course, below 
zero. If, however, the condensation tube was perfectly dry to start 
with, no such trace of aqueous hydrochloric acid remained; that is, 
no water had been carried over from the chloroplatinate. 

A final test of the chloroplatinate was made for water, hydroxyl, 
or oxygen. One hundred grams of potassium chloroplatinate were 
treated exactly as for a determination. The chloroplatinate was 
heated to 400° in a current of dry air, transferred to the apparatus 
used in the determinations, and then evacuated at 350° Next pure 
hydrogen was led over the chloroplatinate imtil it was completely 
reduced. The hydrochloric acid formed was led through a narrow 
U-tube surrounded by a mixture of solid carbon dioxide and alco- 
hol ( — 78®) . Finally the whole apparatus, including the U-tube, was 



362 Bulletin of the Bureau of Standards, \voi. /, No. 3. 

evacuated, the final conditions being 350° in the chloroplatinate 
tube, — 78° in the U-tube and several thousandths millimeters pres- 
sure. Upon weighing, the U-tube had shown an increase in weight 
of 0.9 mg, or I in 30,000, on the hydrochloric acid formed. 

A number of corrections on the weight of the chloroplatinate 
tube were necessary. The first of these were necessary on account 
of the traces of air or nitrogen found in the chloroplatinate tube at 
the end of the determination. These corrections were found nec- 
essary in experiments 4, 5, 6, and 7, their magnitude being 0.35, 
0.76, 0.25, and 2 mg. This air may have been occluded by the 
chloroplatinate, or it may have come from the water of the absorp- 
tion tube. It was immaterial how this correction was applied as 
it lay within the limits of the experimental errors, the maximum 
correction being i : 10,000. 

In the second series it sometimes happened that with the most 
cautious manipulation chloroplatinate was blown over into the 
condensation bulb at the beginning of the experiment. After the 
hydrochloric acid had been absorbed by the water and the appara- 
tus weighed, this chloroplatinate was removed by dissolving in 
water and weighing first as potassium chloroplatinate and then 
again as potassium chloride + platinum, after reduction. This 
correction was applied in experiments 8, 9, and 11, the amounts 
being 2.03, 15.0, and 36.5 mg. The apparent loss of the chloro- 
platinate tube was, of course, diminished by these quantities. 

Hydrochloric acid. — From the agreement of Series I and II 
it seems reasonable to assume that no errors were introduced by 
using water as the absorbing agent for the hydrochloric acid. 

The corrections on the apparent gain of the absorption tube 
were of the following nature: First, the apparent gain was in- 
creased by the hydrochloric acid found in the palladium tube 
and by the hydrochloric acid pumped out from the chloroplati- 
nate tube. The former has been spoken of imder hydrogen. In 
experiments i, 6, and 7 there were found 1.27, 0.8, and 0.15 mg 
of hydrochloric acid, respectively, in the gases pumped out. 

In 8, 9, and 11 the gain of the absorption tube was diminished 
by the amount of the chloroplatinate blown over. The correc- 
tions were 2.03, 15.0, and 36.5 mg. 



Noyes. T 
Wiher.A 



The Atomic Weight of Chlorine. 



363 



The final check on correctness of manipulation, freedom from 
leaks, and other losses was found in the checking of the sum of 
the weights of the hydrogen and chlorine with the weight of the 
hydrochloric acid. In the preliminary experiments of both 
series discrepancies were found until the details of the determi- 
nation had been mastered. On this account and on account of 
other known errors the preliminary determinations were rejected 
entirely. 

RESULTS. 

The values obtained were as follows: The weights represent 
those found after all corrections had been applied. The second 
part of experiment 5 was lost. 



Hydrogen. 


Chlorine. 


Hydrochloric acid. 


At. Wt. CI. 


Mol. Wt HCl. 


1 


0.25394 


8.93293 


9.18695 


35.177 


36.178 


2 


0.28004 


9.85590 


10.13259 


35.195 


36.183 


3 


0.51821 


18.23468 


18.75359 


35.188 


36.189 


4 


0.67631 


23.79587 


24.47123 


35.186 


36.185 


5 


0.58225 
0.47989 


20.48158 
16.88423 




35.177 
35.184 




6 


17.36310 


36.182 


7 i 


0.64132 


22.55816 


23.20054 


35.175 


36.176 



Average of Series I, 35.183 and 36.181. 



8 


0.81608 


28.71691 


29.53167 


9 


0.83194 ' 


29.28055 


30.11207 


10 


0.29074 


13.74926 


14.14078 


11 


0.75560 


26.58427 


27.33926 


12 


0.77518 
Total averag 


27.26746 
e 


28.04110 



35.188 


36.187 


35.195 


36.195 


35.187 


36.188 


35.183 


36.182 


35.177 


36.175 



35.184 (3) 36.183 (7) 



Average of Series n, 35.186 and 36.185. 



The value as found for the atomic weight of chlorine is there- 
fore 35.184 with a probable error of ±0.0013. The value obtained 
for the molecular weight of hydrochloric acid is 36.184 with a 
probable error of ±0.0012. The combined average of both sec- 
tions of the two series is 35.184, with a probable error of ±0.0008. 
This is, of course, on the basis of hydrogen=i. On the oxygen 



364 



Bulletin of the Bureau of Standards. [ voi. 4. no. 3. 



basis this value becomes 35.452 if 11 = 1.00762" and 35.461 if 
11=1.00787." The values for silver calculated from Richards* 
ratio and these two values are, respectively, 107.865 and 107.893." 

The mean values must be considered as most probable at the 
present time. These are 35.457 for chlorine and 107.88 for silver. 

In eleven experiments 6.41925 g of hydrogen were united with 
225.86017 g of chlorine and yielded 232.27288 g of hydrochloric 
acid. The values obtained from these figures are 35.1846 and 
36.1838. 

It may be interesting to note the discrepancies between the 
weights of the hydrogen and chlorine and the hydrochloric acid 
formed in the individual experiments. 





H+Cl. 


HCl. 


Difference. 


1 


9.18687 


9.18695 


f0.00008 


2 


10.13594 


10.13259 


-0.00335 


3 


18.75289 


18.75359 


-fO.00070 


4 


24.47218 


24.47123 


-0.00095 


6 


17.36412 


17.36310 


—0.00102 


7 


23.19948 


23.20054 


-hO.00106 


8 


29.53299 


29.53167 


—0.00132 


9 


30.11249 


30.11207 


-0.00042 


10 


14.14000 


14.14078 


+0.00078 


11 


27.33982 


27.33926 


-0.00056 


12 


28.04264 


28.04110 


-0.00154 




232.27942 


232.27288 


-0.00654 



In these eleven experiments there were seven with an apparent 
loss of weight and four with an apparent gain, the total loss being 
I in 35,000. 

Washington, October i, 1907. 

" Morlcy's value. 

'' Noyes' recent value. 

^^ The values calculated from the results of Dixon and Edgar in the same manner 
are 35.463 and 35.472 for chlorine and 107.90 or 107.93 for silver. The mean 
values 35.467 and 107.91 must be considered for the present as the most probable 
which can be calculated from their work. The values for silver are calculated from 
the results of Richards and Wells, who found that 100 parts of silver give 132.867 
parts of silver chloride. J. Amer. Chem. Soc. 27, p. 525; 1905. 



THE PREPARATION OF CHLOROPLATINIC ACID BY ELEO 
TROLYSIS OF PLATINUM BLACK. 



H. C P. Weber. 



In the work on the atomic weight of chlorine ^ it was necessary 
to prepare considerable quantities of chloroplatinic acid free from 
nitric acid. When using aqua regia to dissolve platinum, consider- 
able diflSculty was experienced in removing the last traces of nitric 
acid by evaporation. When working with as much as loo g of 
platinum, the oft-repeated evaporation to dryness of the solution 
becomes exceedingly tedious, and even at best yields uncertain 
results. If the evaporation is carried on with strong hydrochloric 
acid, considerable quantities of material become necessary, while 
with the use of water there is danger of hydrolytic decomposition 
of the chloroplatinic acid and consequent contamination of the 
chloroplatinate with hydroxychloroplatinates. 

The process here described overcomes these difficulties and yields 
a pure solution of chloroplatinic acid. The platinum is prepared 
for electrolysis by dissolving platinum scraps or platinum sponge in 
aqua regia. The excess of acid is removed either by neutralization 
or evaporation and the platinum solution is reduced by zinc or an 
alkaline formate, preferably the latter. The solution is decanted 
from the precipitated platinum, which is then warmed with a little 
dilute hydrochloric acid to remove iron. The platinum is then 
transferred to the electrolytic apparatus, the washing of the precipi- 
tated platinum being completed in this apparatus, which is con- 
structed as follows. 

It consists of a cylindrical tube about 4 cm in diameter and 35 
cm long, which ends in a narrow glass tube, about 4 mm bore, 

* Noyes and Weber, this Bulletin, 4, p. 345, 1908. 

365 



366 



Bulletin of the Bureau of Standards. \vol /, No. 3. 



"TnRRTffri 



which is given the form of a siphon. The anode is a thin disk of 
sheet platinum which just fits into the tube and is perforated with 
numerous small pin holes. A small piece of platinum wire is welded 
to the disk and carried through the glass tube by means of sealing 
glass. The other end of the platinum wire ends in a glass tube 
which is carried to the top of the apparatus and is filled with mer- 
cury to make connection for the 
current. The platinum disk 
should be about 30 cm from the 
top of the apparatus at that point 
where the tube commences to nar- 
row. After the anode has been 
sealed into the tube the space 
8 below it is filled with glass beads 
to support the platinum disk, 
which should rest firmly and 
evenly upon them. About 5 cm 
from the top of the tube three 
notches are pressed into the glass. 
From these the cathode chamber 
is suspended. This consists of a 
porous porcelain filter about 18 
cm long and 25 mm diameter. 
It is well that the rim of the filter 
fit snugly in the glass tube so that 
the filter cup hangs in the tube 
fairly rigidly. 

The cathode consists of ^ sheet of platinum 4 to 5 cm long and 
2 to 3 cm wide. To it is coiinected a platinum wire passing through 
a glass tube. It is suspended from a perforated watch glass, which 
serves as a cover for the apparatus. 

The whole apparatus is suspended in a long cylinder, by means of 
a large cork, for the purpose of cooling it by running water when 
necessary. This is not shown in the diagram, and may be dispensed 
with when low currents are used. The apparatus has been used 
with a current up to 10 amperes. With a current of this strength 
the cooling jacket is essential, as the apparatus gradually becomes 
hot. 




ANott ..VS.rr-j — — 



n'tder.] Preparation of Chloropiatintc Acid, 367 

The platinum is transferred to the tube, being dropped on the 
anode plate, and is here washed with dilute hydrochloric acid until 
clean. The wash waters are drawn off by gentle suction at the 
siphon end, S, The platinum is then covered with concentrated 
hydrochloric acid. There should be such a quantity of hydrochloric 
acid that the liquid stands on a level with S when the porous cylin- 
der is inserted. The porous cylinder is then inserted and filled to 
the top with hydrochloric acid. After the cathode is inserted the 
apparatus is ready for electrolysis. 

The current may be taken from a 120-volt direct-current lighting 
circuit with a number of incandescent lamps in parallel with each 
other and in series with the cell. The cell may be run continuously 
on 8 to 10 amperes. The current is used quantitatively in dissolving 
platinum. During a run of 4^ hrs at 8 amperes 64 g of platinum 
were dissolved. The theoretical quantity for 36 ampere-hours is 
65 g. While the apparatus is in operation the hydrochloric acid 
travels from the cathode cell to the anode under the influence 
both of gravity and electric endosmosis. With the proper adjust- 
ments of height of hydrochloric acid in the anode cell, the heavy 
layer of chloroplatinic acid solution is delivered at the tip of the 
siphon S, drop by drop. If the flow of concentrated solution sceases 
for any reason it may again be started by gentle suction at S. For 
this purpose it is best to have the siphon tip S connected with a 
receiving flask by means of a double perforated stopper. The acid 
in the cathode chamber is replenished from time to time as it 
becomes necessary. 

If toward the end of the operation, when the amount of platinum 
remaining upon the perforated disk becojnes small, bubbles of chlo- 
rine commence to rise through the liquid, it is an indication that 
the ciurent density is becoming too great. In this case, bringing 
fresh acid into the neighborhood of the platinum black and decreas- 
ing the current will remedy the chlorine evolution. 

In concentrating the solution of chloroplatinic acid after it is so 
prepared, chlorine is passed through it for a short while. This 
insures freedom from platinous compounds in case an}- have been 
formed during the electrolysis. 

Washington, October 8, 1907. 



THE SELFJNDUCTANCE OF A COIL OF ANY LENGTH WOUND 
WITH ANY NUMBER OF LAYERS OF WIRE. 



By Edward B. Rosa. 



The self-inductance of a coil or short solenoid wound with any 
number of layers of wire is given by the formula of Weinstein, or 
Stefan's modification of Weinstein's formula, when one applies the 
proper corrections for the thickness of the insulation and the shape 
of the section of the wire. But for a long solenoid this formula is 
not very accurate. I have elsewhere shown how to obtain the self- 
inductance of a long solenoid wound with a single layer of round 
covered wire or with bare wire wound at any given pitch. I pro- 
pose now to show how one may obtain accurately the self-inductance 
of a solenoid of any length having a uniform winding of any number 
of layers; this will include the case of short coils as well as those 
where the length is too great to be calculated by the formulae of 
Weinstein or Stefan. 

Mr. Cohen gives elsewhere in this Bulletin an approximate for- 
mula for the self-inductance of relatively long coils of more than one 
layer. His formula is convenient in calculation when the number 
of layers is not large, and is accurate enough for most practical 
cases, notwithstanding it assumes the current to be distributed in 
current sheets, taking no account of the shape of the cross section 
of the wire or the thickness of the insulation. I shall now show 
how to calculate accurately the self-inductance of a coil of any length 
and any number of layers, wound with insulated round wire, taking 
account of the shape of the section as well as the thickness of the 
insulation of the wire. 

Let Fig. I be the section of such a winding of mean radius «, 
length /, and depth of winding ^, and having m layers. If n is the 
number of turns per centimeter, 

369 



370 



Bulletm of the Bureau of Standards. 



iVol.4,NQ,3, 



m —nt 

iVj = nl— number of turns per layer 

N — mnl= whole number of turns. 



E^EHI 



T— If 



Hg. 1. 

Suppose the section is divided into squares, as shown in Fig. i, of 
which there will be ljt=zn'. We shall find first the self-inductance 
of a single layer winding of n' turns of square wire, which com- 
pletely fills the section; that is, when the insulation between tunis 
is of infinitesimal thickness. To do this we first find the self- 
inductance Lg of a thin current sheet of //' turns, radius a and length /, 
by Lorenz's formula, which is as follows: 



L, ^ 45^/_' I d (4^i»- /*) E+ dPF^ 8a' I 



(I) 



where d=^4a^+P^ a, /and «' having the meanings explained 

above, and /^ and ^ are the complete elliptic integrals to modulus ky 

i^ f 2a 2a 

where *=-=^^-^j3p^ 

The next step is to find the difference between the self-induct- 
ance Lff for the thin current sheet and the self-inductance L^ for 
the thick current sheet, of thickness / and 7i' turns. Following 
the method given in a previous paper* for a single layer winding of 



*This Bulletin, 2, p. i6i, 1906. 



nosa.] Seif-inductance of a Multiple-layer Coil. 371 

round wire, we have to find 

JL = JL,+JM (2) 

where JL^ is the difference in the self-inductances of the 71' turns 
of square wire making up the thick current sheet and the ;/' turns of 
thin tape making up the thin current sheet; and JM is the corre- 
sponding difference in the mutual inductances. The correction JL 
is to be subtracted from Z,. 

CORRECTION FOR SELF-INDUCTANCE. 

The self-inductance of one turn of thin strip of width / is given 
approximately by the expression 

L',^^ira\ log -^-2 I 

and for one turn of wire of square section 

Z',=47rajlog^-2l 

In the above equations R^ is the geometrical mean distance of a line 
of length / from itself; R^ is the geometrical mean distance of a 
square of side /. 

The difference between these two expressions is 

Z',-Z',=4^a(log^) (3) 

if?,=.44705 /?.=.223i3 

R R 

.'. y =2.0035 and log -^^ = 0.6949 

Hence the difference in the self-inductances of the n turns of the 
thick and the thin current sheet is 

jdL^ = /[Iran [o. 6949] = ^iranA (4) 

We may derive the value of the constant A somewhat more 
accurately otherwise as follows: 



'>^']2 Bulletin of the Bureau of Standards, \voi,4.no.3. 

The self-inductance of one turn of thin tape of width b by Rayleigh's 
formula is 

^'•=H'°^T-i+3-£'(>'*¥+i)} <^' 

The self-inductance of one turn of square wire (of side b) by Wein- 
stein's formula is 

L\=^47ra\^ log ^-. 1.1949+ ^, (log -^ + 0,8777)! (6) 

The difference between these two is 

L',-L\ = 47r J 0.6949 - -g^, Mog -^ + 2.76 jL nearly. (7) 

The first term of this expression is the same as found above (4); 
the second term, depending on the dimensions of the coil, is small 
and may often be neglected. 

If a = 5, and ^=1, this is 

L^g—L\ = 47ra (0.6949— .0027) 
= 47ra (0.6922) 
.-. ^I^ = ^iranAy where A = 0.6922 
Thus the value of the constant A is 0.6949 when bja is ver>' small, 
and decreases slightly (to 0.6922 in this particular case) as dia 
increases. Equation (7) may be used to find its value accurately 
for any given case. 

TABLE I. 

Value of the Constant A as a Function of ia, t being the depth of the 
Winding and a the Mean Radius. 





ta 






A 

0.6949 








0. 












0.10 






0.6942 








0.15 






0.6933 








0.20 






0.6922 








0.25 






0.6909 







Xasa.] 



Self-inductance of a Multiple-layer CoiL 



373 



CORRSCTION FOR MUTUAL INDUCTANCE. 

The correction for mutual inductance is nearly the same as for a 
single layer winding of round wire. It would be exactly the same 
if the geometrical mean distance of square areas from each other 
were the same as for circular areas. This is true almost exactly 
except for very near areas, as the adjacent turns. Table VIII of 
my previous paper * gives the values of the constant B for round 
wires, and these values may be used in this case without serious error. 
The correction depending on mutual inductances is 

JM = ^iranB (8) 

To obtain somewhat more accurate values of B we should use the 
values of the geometrical mean distances of square areas, as shown 
in column 2, Table II. These are sensibly the same as for round 
areas beyond a distance equal to five times the diameter of the 
squares. Hence only the first five values of S in Table I differ from 
those of Table III * of the previous paper, referred to above. 

TABLE II. 

Table of Geometric Mean Distances and Corrections Depending upon 

Them. 





0. M. D. R for Tapes 


0. M. D. R'for 
Squares 


Ratio. J;-^/ 


«-log» 




R, =0.89252 


1.00655 


1.12776 


0.12025 




R,=1.95653 


7.00102 


1.02274 


.02249 




R3=2.97171 


3.00030 


1.00962 


.00958 




R4=3.97890 


4.00013 


1.00531 


.00530 




R5=4.98323 


5.00007 


1.00337 


.00337 




R«=5.98610 


6.00003 


1.00233 


.00233 




R7=6.98806 


7.0000 


1.00171 


.00171 




R8= 7.98957 


8.0000 


1.00131 


.00131 




R^,=8.99076 


9.0000 


1.00103 


.00103 



From these values of S and the succeeding values as given in 
Table III * we can calculate the table of values of B^ corresponding 



'This Bulletin, 2, p. 161. 



374 Bulletin of the Bureau of Standards, \voi. /, N0.3. 

to Table VIII for round wires. The constant B is given by 

TABLE III. 

Values of Correction Term B, Depending on the Number of Turns of 
Square Conductor on Single Layer Coil. 



No. of Turns 


B 


No. of Turns 


B 


1 


0.0000 


16 


0.3017 


2 


.1202 


17 


.3041 


3 


.1753 


18 


.3062 


4 


.2076 


19 


.3082 


5 


.2292 


20 


.3099 


6 


.2446 


21 


.3116 


7 


.2563 


22 


.3131 


8 


.2656 


23 


.3145 


9 


.2730 


24 


.3157 


10 


.2792 


25 


.3169 


11 


.2844 


26 


.3180 


12 


.2888 


27 


.3190 


13 


.2927 


1 28 


.3200 


14 


.2961 


29 


.3209 


15 


.2991 


30 


.3218 



EXAMPLE 1. 



As a first example let it be required to find the self-inductance of 
a coil of mean radius a = 5 cm, length /= 10 cm, depth of winding 
/= I cm, and uniformly wound with 10 turns of wire per cm, having 



— i^m — 



\^ 



a*5 

I 



lA, 



^««.] Self-inductance of a Multiple4ayer Coil. 375 

therefore 10 layers of icx) turns per layer, or a total of 1,000 turns. 
We first find the self-inductance Z, of a current sheet of 10 turns, 
radius «=5, /=io. 

Using formula (i), we have the following values: 

rf=Y4^*+^' =V2oo >^=-^ = -^2 = sin 7 

4a«-/«=o .-, 7=45° 

«' = io 

«'//= I 

Hence 

Z,= ^jl000V2 ^--8XI25[=^^^L2 ^-1} (10) 

The value of ^ for 7 = 45° is 1.85407. Substituting in 

Z,=^^ ttI 1.62205 i=2i62.737rcni 

To find the correction JL we must have the two constants A and 
B. By equation (7), or Table I, ^ = ,6922. By Table II, B = .2792. 
Hence 

^jZ = 47ran(A + B) 

= 2009r(o.6922+.2792) 
= i94.287rcm 
Z„ = Z,— -*^iZ=i968.457rcm. (11) 

Thus the thick current sheet (10 cm x i cm) of 10 turns has a self- 
inductance Z^ about 9 per cent less than that of a thin current 
sheet Lg of the same length and radius equal to the mean radius of 
the thick sheet. 

If the coil were wound with 1,000 turns of square wire (the insu- 
lation being of infinitesimal thickness), then the current would be 
uniformly distributed over the entire section of the winding, and the 
self-induction would be 100* times as great as for 10 turns, being 
proportional to the square of the number of turns. In general, we 
get the self-inductance for m layers by multiplying the value for one 
layer by w*. This, of course, supposes a uniform winding such that 
m layers occupy as much space vertically as m turns horizontally on 
15298—08 3 



376 Bulletin oj the Bureau of Standards. ir<fi. 4,^0.3. 

the coil. In this case the self-inductance will be 

Zy — i968.457r x 10* cm 
= i9.68457r millihenrys 
= 61.841 millihenry's (12) 

The subscript u signifies unifonn distribution of current over 
the entire cross section of the coil. We must now find the self- 
inductance L for this coil when wound with 1,000 turns of round 
insulated wire. Suppose the bare wire to be 0.8 mm in diameter, 
the covering being o.i mm thick; there will be three correction' 
terms to apply, C, F^ and E^ each of which gives an increase in L, 
The first expresses the difference in Z, due to the wire being round 
instead of square, as previously assumed; the second expresses the 
difference in Z, due to the wire being of smaller diameter than if 
there was no appreciable thickness of insulation; the third expresses 
the corresponding difference in the mutual inductances. 
The sum J^L is then as follows: 

J^ = 47rna( C+ F+ E) 

C= 0.1 381 for the case of round wire. 

/^=o.223i = log^ ^ = logg 1.25 in this case. 

-£'=0.0172 for this size and shape of section.' 
C+i^+'i5'= 0.378^ 

.-. ^^=47rX 5000 [0.3784] 

= 75687r cm = 23776 cm 

= 0.0238 millihenrys 

This correction J^L amounts in this particular case to about 4 parts 
in 10,000 of L, We have now finally 

Z=Z„+^,Z= 61.865 millihenrys (13) 

The same method may be used for a coil of any length and any 
number of layers. 

EXAMPLE 2. 

As a second illustration of this method of calculating the self- 
inductance of a coil of any number of layers let us take a very short 

*This Bulletin, 8, pp. 34 and 37, 1907. 



Rosa.^ Self-inductance of a Multiple-layer Coil, 377 

coil and check the result by the formula of Stefan. Let the mean 
radius be 10 cm and the cross section of the winding i x i cm. For 
the self-inductance L^ of the current sheet of radius a and length 
b we will this time use Rayleigh's formula, which is very accurate 
where b\a is as small as i/io. Rayleigh's formula is 

Here — =80 log^ 80= 4.382027 



b 



b' 



.8 



^2^*- ^200- • ^2a"*0''^^ 8o+-J= ^0001448 

32^ 3200 Z2a \ 4/ 4.383475 

-•50 



.3-883475 

.•.Z, = 47r^iiV*x 3.883475 

This is the self-inductance if the current is condensed into a ring 
of zero thickness; that is, ^i = io, *=i, ^=0. By equation (7) the 
correction term yi = 0.6941 5 (see also Table I) and -ff=o, since 
«' = I (Table III). 

.-. jd^L =47r^iiV(.694i5) 

Z„==Z,«—^,Z,=47r^iV*x 3.18932 cm. (14) 

If A^=4oo= 20 turns per cm and 20 layers, we have for Z„, a being 
10 cm, 

Z^ = 6400000x3.18932 cm 

= 64.125 millihenrys. (15) 

This is the self-inductance if the wire is square and fills the entire 
section. The corrections C, -F, and E must be applied as in example 
I to reduce to the actual case of a winding of round, insulated wire. 
In this case, supposing the bare wire is 0.3 mm in diameter, and 
hence D\d= 5/3. 

C= 0.1 381 

7^=0.5108 

£"=0.0176 

C+ 7^+ £=0.6665 



378 Bulletin of the Bureau of Standards, iyoL4.J^'o.j. 

.\ ^^=4irna (C+J^+E) 
= l6cxx>ir X 0,6665 
= 33>502 cm. 
= .0335 inillihenrys 
.-. Z=Z.„+^^= 64.1585 millilienrys. (16) 

We can check the value of Z^ by the formula of Weinstein or 
that of Stefan. These formulae assume the current to be uniformly 
distributed over the section of the coil; that is, that the wire is 
square and fills the entire section. 

Stefan's formula is as follows: 



^=H('+w*>'*vfe-^'+i&'l *■'> 



In this case a=io, 6=c=i j/, =0.84834 j',= 0.8162 
, 8« , 80 



(^ + ^K"= ^•°3^^3 



.y^= 0.00051 



16a 

4.03764 
>'i= -084834 

3.18930 
.-. Z.„ = 47r^^X 3.18930 (18) 

This differs from the value found above (14) for L^ by less than 
I part in 100,000. 

It is of course to be expected that these two methods of obtaining 
Lu would agree, from the method of obtaining the correction term 
A. But an actual numerical test is nevertheless not superfluous. 

When the coil is long, so that Stefan's (or Weinstein's) formula 
does not apply, the method given above for obtaining L^ from Lg is 
the same and just as accurate provided the correction term B is 
accurately known. That term here differs very slightly from its 
value for single layer coils where it has been already verified, so we 



jfasa.] Self4nductance of a MuUiple-layer Coil. 379 

may be sure that L^ and so also L for any winding may be obtained 
with great precision by the above method. 

Let us now use this method to determine the magnitude of the 
error in results obtained by Stefan's formula when applied to coils 
longer than those for which this formula is accurate. 

EXAMPLE 3. 

«=io, b=io^'C=i 

By Coffin's formula (extension of Rayleigh's) we have 

Lg=/[iraN^ (1.57944+.07280— .00138+.00009) 

=:47raiV^X 1.65095 (19) 

A = .6942 as before 
^=.2792 Table II 

y4+^=.9734 

^iZ=47r^i«'x(.9734) 

Here «' = */^=io, and hence A-^-B must be divided by 10 to put 
the correction in the same form as Lg, That is, if n = 10, 
J^L^^iran'^ [-09734] 

Therefore, \i n' = N we have 

L,,=^L,'-J^L^/[iralsr [1.5536] (20) 

So far we have assumed the section 10 x i cm to be divided into 10 
squares. But N may now be any number, and the above expression 
L^ gives the value of the self-inductance, assuming the current is 
uniformly distributed over the section. 

Another way of putting it is to put « = w*«', where m is the 
number of layers and mn' is the number of turns per layer. In the 
above example n = 10. It is always bjc. The correction J^ L is 

J^L = ^7ran' {A+B) for //' turns 
.-. J,L=47ran'*(^^i^\ for «' turns 



380 Bulletin of the Bureau of Standards, \^voi. 4. i^'o. 3. 

But if the winding instead of being one layer of n' turns is m layers 
of n^n* turns, the self-inductance and also the correction J^ L will 
be m*^ times as great. Therefore 



^,L=4-^amW^-^'^ 



\m 



= 47raJV^\ -f — since N- 



(21) 



Hence (A+B) is always divided by //'. In example 2, «' = i. 
By Stefan's fonnula we have, since jVi = 0-59243, Js= 0.1325 

L, = 4'^aJV' l( I + -3^) 2.074467-0.59243+^f-^l 

= 47r^ZiV*X 1.55536 (22) 

This is I part in 900 more than the value obtained above (20) by 
the more accurate method, showing that Stefan's formula is not 
seriously in error for a coil whose length is equal to its radius, but 
it is much less accurate than for short coils, as its method of deriva- 
tion requires. 

For a coil only half as long (^ = 5, c= i) the difference between 
the two methods is only one part in 4,000, while for a coil twice as 
long (A =20, ^=1) the difference is about i per cent. That is, 
Stefan's very convenient formula is correct to within i per cent 
for a coil whose length is as great as its diameter. Beyond that the 
error increases rapidly. 

SUMMARY. 

To recapitulate the method set forth in the preceding pages for 
obtaining the self-inductance of a coil wound in the ordinary man- 
ner with insulated round wire, we have the different self-inductances 
to consider, Z,„ L^, and Z, which are related as follows: 

Lg is the first approximation to the self-inductance required, and is 
obtained by the current sheet formula of Rayleigh, Coffin or Lo- 
renz.* It is the self-inductance of a coil of length /, radius j, 

♦This Bulletin, 2, p. 186. 



Jiosa.] Self'inducta7ice of a Multiple-layer Coil. 381 

having A^ turns, but the depth of the winding t is supposed redticed 
to zero, 

jd^L is the correction to apply to L^ to obtain L^^ which is the 
self-inductance of the coil of same dimensions and number of turns, 
but with actual depth t of winding; the current is, however, now 
supposed to be uniformly distributed over the cross section of the 
winding, as though the wire were of square section and had only 
an infinitesimal covering. ^^L depends on two terms, A and B, 
A is found from equation (7) and B from Table II. 

The actual self-inductance of the coil L differs from L^ by the 
correction ^^Z, which depends on three correction terms, C, F^ and 
E. The determination of these quantities, which depend on the 
shape of the section of the wire, the thickness of the insulation, the 
number of turns of wire in the coil, and the shape of the section 
of the coil, has been fully discussed elsewhere' and their values 
given. The correction J^L is much smaller than ^jZ, and can 
be neglected except when the highest accuracy is sought. The 
value of L^ and jd^L can be calculated with accuracy if the dimen- 
sions are accurately known, and this is possible if one uses enameled 
wire of uniform section arid takes piroper care in winding and meas- 
uring the coil. However, such a coil can not be recommended for 
a standard of the highest precision, and I have given the full theory 
for the sake of completeness and to show the magnitude of the 
smaller corrections, rather than because all the corrections are 
likely to be generally needed in practice. 

Washington, October 12, 1907. 

* This BuUetin, 8, pp. 3, 4, 28-37. 



SELF-INDUCTANCE OF A SOLENOID OF ANY NUMBER OF 

LAYERS. 



By Louis Cohen. 



The only formula heretofore available for the calculation of the 
self-inductance of a long coil or solenoid of more than one layer is 
that of Maxwell, which is as follows: 

L^^v'n^lix-y) (;r»-/) (i) 

where / is the length of the solenoid, n is the number of turns per 
unit length, x and y are the external and internal radii of the sole- 
noid. This formula, however, was developed on the assumption of 
a uniform field within the coil, which means that the end effects 
can be neglected. The assumption may lead to an error as great as 
12 per cent as I shall show later, even in the case of a compara- 
tively long solenoid, when the length is ten times the radius. It is 
quite evident that such a formula is not of very great value where 
accurate results are desired. It is, however, a very simple and con- 
venient fonnula for numerical computations and is useful when only 
a rough approximation is desired. 

I propose to develop in the following pages a formula for the self- 
inductance of a solenoid of any number of layers, and which will 
give results accurate to within one-half of i per cent even for a 
short solenoid, where the length is only twice the diameter, the 
accuracy increasing as the length increases. For most practical 
cases this degree of accuracy is amply sufficient. 

Suppose we have a solenoid of m layers, the mean radius of the 
first layer being ^z^, and of the last layer a^^ then the self-inductance 
of the solenoid will be given by the following expression: 

383 



384 Bulletin of the Bureau of Standards. ivol. /, N0.3. 

L = L,+L,+L, + +L^ 

+ 2[M,,+M,,+ +M,^ 

+ M^+M,,+ +M^ (2) 

+ M^+M,,+ +M^ 

+ 

+ 

Zi, Z,, Zj, etc., are the self-inductances of single layer solenoids 
whose mean radii are a^^ «g, a,, etc., and the Ms are the mutual induc- 
tances between the various single layer solenoids. We have various 
formulae for the self-inductance of a single layer solenoid, and also 
for the mutual inductance of two coaxial solenoids,' and if after 
substituting the various values for L and J/, we can combine them 
so as to give a simple expression, we shall evidently have a useful 
formula for the self-inductance of a solenoid of m layers. 

In a previous paper* I have developed an absolute formula for the 
self-inductance of a single layer solenoid, which is as follows: 

a is the mean radius, / is the length of the solenoid, and n is the 
number of turns of wire per centimeter, F and E are the complete 
elliptic integrals of the first and second kind to modulus ^, where 

This formula was first given by Lorenz without, however, giving 
its derivation. FsnA E can be put in the form of series, thus: 

2 1 2* 2.V 

» This BuUetin, 8, p. 305. « This Bulletin, 8, p. 303. 



CokeH.] Self'tndMctance of Solenoids. 385 

If /=4^, then ^•= — = -, and the term in ^* will be only about — 
^ ' 20 5 ^ 200 

which may be neglected if we are aiming at an accuracy of only one 

half of a per cent. For longer solenoids the accuracy will of course 

be higher. Using, therefore, only the first two terms of the above 

series, and introducing the value of k ', we get: 

Introducing the values of F and E into equation (3) and simplifying 
•we obtain 

This is a very simple and convenient approximate formula for the 
calculation of the self-inductance of a single layer solenoid. 

The self-inductance of a solenoid is a function of its radius, hence 
if we denote by L^ the self-inductance of the central layer solenoid, 
the self-inductance of the various other layers will be given by the 
following formulae: 



t- 



- f-- r 



^,_.=A- I "da'^- I S^« 






ll+l 



fVz r»^ dr 



386 Bulletin of the Bureau of Standards. \yoi. 4, N0.3. 

Usually the winding is of comparatively fine wire, say, o.i to a 2 
cm., and therefore the value of any of the above integrals will be a 
small quantity as compared with L^, and the difiEerence between any 
two of the above integrals will be an exceedingly small quantity. 
In summing up the self-inductances of the various layers, we evi- 
dently have as many negative as positive integrals which will nearly 
^ cancel each other and therefore: 

2 Z=;;.A=;;.4-'«|^-.;q:^^--J-) (s) 

when ao is the mean radius of the solenoid. 

It remains now to find the value of B of equation (2). The 
mutual inductance between two coaxial solenoids is given by the 
following expression' 

Ar=47r^«« [/-2^a] 
where 

I'-r+A 



a = - 



2A 



a« / A\ a' / 2A' 5A\ 

IiJ-(-7^)-6^(^+7r-77r)+---- 



r=^A*+Py A is the radius of the external solenoids, and a is the 
radius of the internal solenoid. Since, however, we are only aiming 
at an accuracy of one-half per cent for short solenoids we may put 

l-r+A a^ 



a=- 



2 A 16A 



and neglect the other terms. Introducing this value of a we get: 

il/=47r^^v{v^*T/*-^ + £^} (6) 

Putting ^g=^i+&z,a3 = ^Ji + 2&2, am=a^+ (w—i)&z where 

Ba is the distance between two consecutive layers, and also expand- 
ing the term under the radical and neglecting small terms, we 
shall have : 

' MaxweU, Electricity and Magnetism, II, § 678. 



Cohen.] Self-inductance of Solenoids, 387 



~ ~8— f 
2CL*ha ^ a 1 

JI/„=4^a.v{v^7+^+;^^=^-«,-4S«+|} 

, «i (>«-5)&^l 
"^8" 8 I 



388 Bulletin of the Bureau of Standards. \voi.4,no.3. 

1*- J « «f /— i — TT (m—i)aJba , .. a. 






Summing up we get: 



-«.--8a+g-~ -g 



.]/„+J/„+ .... +J/^„ = 4^a.V(»i-2){v^7+7»+^^^^-a. 



(z«+i)&j! a, (»i— 3)8a 
" "^ +8 2" " 8 



.1/,,+.!/,..+ +J4„.=4^a»-3)|v«?+/'+^^^.^^^|^ 



(w+2)&e a, (»/— 4)&i 
2 +8 r~ 8" 



^^/m+^J^m+ +^1/..». = 4tV«'('«-4){v«,'4T'+^^^J^- 



(>"+3) . , g. (»^-5) H 



Adding all the stimmation terms we get for the total mutual induc- 
tance between the various layers: 

2 .l/=4,i'«'j[(w-iK+(««-2K+('«-3K+ • • • • ](v«?+^* 
-'^^a\-\-^\m{m—\)a*^-{m—\){m—2)a*-\-{ni-2){m—T^* 



cok^m] Self-inductance of Solenoids, 389 

The final formula for the self-inductance of a solenoid of m layers 
will therefore be as follows: 

Ua,*+/*-|«i)+ \ [nt{m-i)a*+{m-i){m-2)a,*+ . . .] 

{^^^,-^)-l{.»»i»^-^W+(^-2){m-3)a'+...]^ (7) 

The last term in equation (7) is only about 1/500 of the total induc- 
tance even in the case of a relatively short solenoid, where the length 
is twice the diameter, and hence we may neglect the last term. We 
therefore have: 

( VV+? - I «.)+ 1 \nt(fn- iK+ . . ^(^li^ - ««)} (8) 

For long solenoids, where the length is, say, four times the diam- 
eter, we can neglect also the last term in equation (8). 

The formula for the self-inductance as given by equation (8) is a 
simple one and very convenient for numerical computations. 

Below are two numerical examples to show the per cent of error 
that Maxwell's formula (i) will introduce: 

EXAMPLE 1. 

^1=5 cm, Sa=o.i cm, ^=4, ^0=5.15 cm, /=so cm. 

Introducing these values in (7) we get: 

Z=47rV{484i.9+i4i34.7— 45.9— 4.4}=47r^«'x 18926 

It is seen that in this case where the length is five times the diam- 
eter, even the third term of equation (7) is only about one four- 
hundredth part of the total inductance, which may be neglected in 
approximate calculations. 



390 Bulletin of the Bureau of Standards. [Ko/./,m»j. 

The same example calculated by Maxwell's formula gives 
Z,=47r^«"x 21228 
The error is a little over 12 per cent. 

EXAMPLE 2. 

-4i = 5cm, &i=o.2cm, w^ = 5, «o=54cm, /=20 
By formula (7) 

Z = 47r"«" {2271. 5+8795.9— i6i.5—i8} = 47r^«'x 10888 
By Maxwell's formula (i) we get for this case: 

Z=47r^«'x 14622 
The error in formula (i) is therefore about 35 per cent 
Washington, October 11, 1907. 



INSTRUMENTS AND METHODS USED IN RADIOMETRY. 



ByW.W.Coblcntz. 



I. Introduction _ 392 

II. The Microradiombter - 394 

III. The Radiomicrometer 395 

IV. The Thermopile 398 

1 . Comparison of an old and a new form of Rubens thermopile 400 

2. Losses due to the Peltier effect... 401 

V. The Radiometer 404 

I Comparison of sensitiveness and area of vane 405 

2. Comparison of sensitiveness and diameter of fiber suspension 406 

3. Comparison of sensitiveness with wave-length of exciting source. . 409 

4. Comparison of radiometer with bolometer 411 

5. Some points in radiometer construction 413 

VI. The Bolometer with its Auxiliary Galvanometer. 415 

1. Historical 416 

2. The construction of sensitive galvanometers 424 

(a) Form of coils 425 

(6) The needle system ^. 428 

(c) The assembled galvanometer 430 

(rf) Sensitiveness of galvanometer 430 

(e) Proportionality of galvanometer deflections. 432 

(/) Magnetic shielding ._ _ 434 

3. The construction of sensitive bolometers 435 

(a) Best resistance of bolometer and of balancing coils _ . 437 

4. Design of a bolometer 438 

5. Comparison of sensitiveness of bolometers 445 

6. Comparison of bolometer with thermopile 447 

7. Bolometric usage 450 

(a) Errors resulting from lack of balance of bolometer 453 

VII. Selective Radiation Meters 454 

VIII. Change op Sensitiveness op Instruments 455 

(a) Experiment with sectored disk 455 

IX. Summary _ _ _ 459 

15298—08 4 391 



392 Bulletin of the Bureau of Standards, [Voi. 4,^0.3. 

L mXRODnCTION. 

There are few fields of experimental investigation so beset with 
difficulties as the quantitative measurement of radiant energy. 
This is due chiefly to the fact that the radiation to be measured is 
generally from a surface, of which it is practically impossible to 
determine the temperature. The measurement of radiant energy, 
moreover, generally involves its transformation into some other 
form, and the receiver used for this purpose is subject to losses by 
heat conduction within, and by reflection, radiation, and convec- 
tion losses from its surface. 

As a result of inquiry into the development of the various 
instruments and methods used in measuring radiant energy, viz, 
the radiometer, the thermopile, the radiomicrometer and the 
bolometer with its auxiliary galvanometer, the writer has accu- 
mulated data, part of which are included here, with the hope that 
it may be useful to others interested in the subject. An attempt 
is also made to give the general principles involved in the con- 
struction and use of different radiation meters, as well as original 
experimental data of their relative efficiencies. 

Much has been written on the theory and design of sensitive 
galvanometers and bolometers, and nothing radically new will be 
attempted in this paper. Not that improvements are impossible, 
but, as will be noticed presently, the working sensitiveness seems 
to have attained a fixed value for all of the various designs of 
galvanometer coils and magnet systems thus far described. It 
will also be noticed that the ** working sensitiveness,'* at which 
it is possible to use the instrument with precision and convenience, 
and the highest attainable sensitiveness are two distinct factors 
in rating radiation meters. For example, it may be possible at cer- 
tain horn's of the day to read a bolometer-galvanometer deflection 
to o.i mm. and thus detect a rise in temperature of, say, one ten- 
millionth degree, but for an instrument that is useful at all hours 
a fair estimate of the sensitiveness attained by various observers 
is about one-tenth to one-twentieth this value. It is practically 
impossible to buy instruments as sensitive as this. While galva- 
nometers and thermopiles can be purchased, they often fall short 
of the specifications of the original, so that it is better to build the 




cobitntx.] Instruments and Methods of Radiometry, 393 

instrument in one's own laboratory. Here again one experiences 
the difficulty that the descriptions of such galvanometers and 
bolometers are scattered through so many journals that it becomes 
a burden to learn of the different improvements that have been 
made. For example, one may find a galvanometer with large 
coils, and a heavy magnet system, provided with an excellent 
magnetic shield. Again, one will find a galvanometer with small 
coils, and light suspension, built in such a manner that the latter 
is visible, which is a desirable feature, but the whole is enclosed in 
a large glass case which renders magnetic shielding very difficult. 
Furthermore, European investigators have used their bolometers 
and balancing coils in separate cases, and the bridge arms of equal 
resistance, while the latest developments in this country show 
that it is best to have the resistance of the bridge arms several 
times that of the bolometer strips, and the whole, including the 
balancing wire, enclosed in a single double walled case. These 
are some of the facts brought out by the writer's inquiry into the 
matter; and in designing the instruments to be described, and in 
the improvements suggested, an attempt was made to include as 
many as possible of the good points in the various instruments 
previously described, and to introduce simplifications wherever 
possible. 

Various instruments for measuring . radiant energy have been 
devised, the relative sensibilities of which can be rated without 
further investigation. That in many cases the sensitiveness has 
been overestimated will be noticed in the present paper. Four 
instruments, viz, the radibmicrometer, the thermopile, the bolom- 
eter, and the radiometer have been used extensively in radiation 
work, and in each case the investigators have found qualities 
which seemed to render each type of instrument superior to the 
others. But, so far as the writer has been able to learn, all four 
instruments have not been heretofore studied by any one person. 
Each instrument requires a special mode of handling, and has 
pecuUarities which can be learned and controlled only after pro- 
longed use. This is particularly true of the radiometer, and of 
the bolometer with its auxiliary galvanometer. Having already 
had considerable experience with radiometers, one of which was 



394 Bulletin of the Bureau of Standards, \vol 4^^0.3. 

the most sensitive yet constructed,* the writer has, in this exami- 
nation, devoted most of his attention to the bolometer. The 
investigation originated for the most part from the question 
whether the radiometer was selective in its action in the region 
of short wave-lengths. In previous work it was found that the 
radiometer gave small deflections in the violet spectrum of the 
arc where Snow,* using a bolometer, found large deflections. 

In the course of the discussion it will be noticed,' as was pre- 
viously known in a general way, that each instrument has some 
quality which makes it useful for particular kinds of work. For 
measuring very narrow emission lines and determining dispersion 
curves the bolometer is no doubt the best instriunent. For 
measurements requiring a larger receiving surface the linear 
thermopile is the more sensitive and the more precise. It has 
the further advantage that there is no permanent current. On 
the contrary, the bolometer has a current which heats the 
bolometer strips above the temperature of the surrounding air. 
This causes air currents which make the zero of the galvanometer 
unstable. This is not true of the thermopile. Less is known 
concerning the radiometer, which rivals the bolometer and the 
thermopile in sensitiveness. Furthermore, the radiometer is not 
subject to magnetic perturbations. Its window limits its useful- 
ness to the region of the spectrum up to 20 ft. The fact that it is 
not portable is a minor objection. 

An attempt is made in the present paper to discuss all the 
important details involved in radiometry, so that it will be pos- 
sible to gain a knowledge of the subject without searching through 
the already extensive literature. 

II. THE MICRORADIOMETBR. 

Since we are concerned with radiation meters of the greatest 
sensitiveness, the ingenious device of Weber,' called the ** micro- 
radiometer,'' deserves notice. The instrument is not unlike a 
combination of a differential air thermometer and a Wheatstone 
bridge. Two arms of the bridge consist of a thin glass tube con- 

* See "Investigations of Infra-red Spectra," Part II. A still greater sensibility 
was attained in the present investigation. 
^ Snow, Physical Review, 1, p. 32; 1893. 
' Weber, Archiv. Sci. phys. et Nat. (3), 18, p. 347; 1887. 



codieniz.] Instruments and Methods of Radiometry, 395 

taining a drop of mercury at the center, with a solution of zinc 
sulphate at the ends, into which dip platinum electrodes. The 
ends of the glass tube widen out into large bulbs containing air. 
The ends of the bulbs are covered with rock salt windows. If 
radiant energy is allowed to enter one of the bulbs, the air ex- 
pands and pushes the liquids toward the opposite bulb. This 
will change the relative lengths of the column of mercury and of 
the solution between the platinum terminals, which means a 
change in resistance in the bridge arm and a consequent deflec- 
tion of the galvanometer. The instrument was stated to be 
sensitive to a temperature change of 0000 01?, and while it is not 
adapted to spectrum radiation measurements, it might be used 
in total radiation work where an elaborate installation is not con- 
venient. By making the receiving bulb of opaque nonconducting 
material and covering the inside with lampblack, or platinum 
black, this would be as complete an absorber (black-body) as the 
thermopile or bolometer. Its efficiency would of course depend 
upon the gas enclosed. 

m. THE RADIOMICROH£TER. 

The radiomicrometer is essentially a moving coil galvanometer 
having a single loop of wire with a thermo- junction at one end. 
This instrument was invented independently by d' Arson val * and 
by Boys.* The former used a loop, one part of which was silver 
and the other was of palladium. The latter used a junction of 
bismuth and antimony, which was soldered to a loop of copper 
wire. 

The sensibility of the Boys instrument was given as tit ^i-^ irTTTr 
to ^T v^Tjvir of I®. From subsequent work with other radiation 
meters in which this high degree of sensitiveness has never been 
attained, it would appear that the sensibility of the radiomicrom- 
eter was overestimated. It certainly has never attained the 
sensibility of the radiometer, one example of which, used by 
Nichols (loc. cit. Table III), was 12 times as sensitive as the 
radiomicrometer of Boys. The latter gave a deflection of a 

* d'Arsonval, Soc. Franc, de Phys., pp. 30 and 77; 1886. 

* Boys, Proc. Roy. Soc, 42, p. 189, 1887; 44, p. 96, 1888; 47, p. 480, 1890; Phil. 
Trans., 180 A. p. 159, 1889 



396 Bulletin of the Bureau of Standards. [roi.^.jvo.j. 

little less than i cm per mm' of exposed vane for a candle and 
scale each at a distance of i meter. Paschen* attempted to 
improve the radiomicrometer, but out of about fifty jimctions only 
three were useful, and these were only three times as sensitive as 
that of Boys, while the period was about forty seconds. The 
long period is not always detrimental, however, for the radio- 
micrometer is not subject to magnetic disturbances and is a very 
useful instrument for work not requiring the highest attainable 
sensitiveness. The writer' has indicated further improvements 
in the instrument, and places it in a vacuum, which increases the 
sensibiUty by at least 70 per cent. The instrument was about 
six times as sensitive as that of Boys for a full period of 25 sec- 
onds. Para- and dia-magnetism limited the sensitiveness to 
this value. The work with this instrument brought out the fact 
that one may use too strong field magnets and that further im- 
provement may be made by using weak magnets, or by using 
narrow strong magnets situated as far as possible above the 
thermojimction,so as to avoid the effect of para- or dia-magnetism. 
The combination of the radiomicrometer and the radiometer is 
feasible, although the writer found its usefulness as limited as 
that of the radiomicrometer. When wires can be obtained more 
free from magnetic material it will be possible to construct a more 
sensitive instrument. It is doubtful, however, whether it will 
ever surpass the bolometer used with a galvanometer of the 
highest sensibility. With the radiomicrometer, Lewis* was able 
to investigate infra-red emission spectra of the alkali metals, 
which are weak in energy. Wilson • and Julius *® have used the 
radiomicrometer for total and spectrum radiation work, and 
found the instrument highly satisfactory. The long period 
(which also obtains in other sensitive radiation meters) and lack 
of portability, mentioned by some writers, is certainly not to be 
weighed against its indifference to magnetic perturbations and 
constancy of the zero reading. Even a slow period is less ob- 
jectionable than a quick-period instrument with which just as 

•Paschen, Ann. der. Phys. (3), 48, p. 272; 1893. 

' This Bulletin, 2, p. 479; 1906. 

* Lewis, Astrophys. J., 2, p. i; 1895. 

•Wilson, Proc. Roy. Soc., 56, 1894; 68, 1895; 60, p. 337; 1896 

'° Julius, Handlingen, 5, de Nederlandisch Natuur en Geneeskundig Congres; 1895. 



CobUntz.] 



Instruments and Methods of Radiometry, 



397 



much time is lost by repeating observations, which may be affected 
by the lack of constancy of the zero. The instrument is self- 
contained and where the greatest sensitiveness is not required, 
it deserves a wider application. In Table I are given the various 
radiomicrometers thus far described and their sensitiveness, 
expressed in centimeter deflections per mm* of exposed vane, 
for a candle and scale each at a distance of i meter. 

It will be shown below that the highest efficiency is obtained 
when the resistance of the thermocouple is equal to the combined 
resistance of the connecting wires and of the auxiliary galvanom- 
eter. Since the resistance of a single couple is much less than 
that of the galvanometer, it is most advantageous to use several 
pairs of junctions. On the other hand, in the radiomicrometer 
the connecting loop of wire has a negligible resistance, and hence 
there is no advantage in using more than a single pair of jimctions; 
for as we increase the electromotive force by adding jtmctions 
the resistance is increased in like proportion, so that the current 
remains practically constant. For like reasons there is no ad- 
vantage in using more than one turn of wire in the connecting 

loop. 

TABLE I. 

Sensitiveness of Radiomicrometers and Rubens Thermopile. 



Observer 


Pull period 


Area of vane 


Deflections in cm/mm * 
candle and scale at z m 


BOYB 


10 sec. 

40 

20 

40 
25 


4mm« 


0.9 cm. 


Phil. Trans., 180 A, p. 159, 1889. 
Paachen 


3 


Wied. Ann., 48, p. 275, 1893. 
Lewis 


1.4 

3 
3 


1.3 (?) 
3.6 


Astrophys. Jour., 2, p. 1, 1895. 
Coblentz 


ThisBnnetin 


6 (in vacuo) 


2, p. 479, 1906. 


Thermopile. 


Rubens 


14 


16(?) 


16(250cmtotaldeflection) 
1 mm=l?lxiO-«C. 


Wied. Ann., 46, p. 244, 1898. 



39^ Bulletin of the Bureau of Standards, \voi 4.N0.3. 

IV. THE THERMOPILE. 

The thermopile has been in use from the very beginning of 
radiants energy measurements, and in the hands of Tyndall and 
other pioneers in this domain has rendered excellent service in 
spite of its great heat capacity. For spectro-radiometric work, 
however, only the linear thermopile of Rubens" is well adapted. 
This thermopile consists of 20 junctions of iron and constantan 
wires about o.i mm to 0.15 mm diameter (resistance 3.5 ohms), 
and when used with a galvanometer, having a figure of merit of 
i=: 1.4X10"*" amperes (resistance =3 ohms, period =14 sec- 
onds) a deflection of one scale division indicated a temperature " 
change of i?i x lo"'. A candle at 5 m gave a deflection of 
about 10 cm or 250 cm at i m. The area of exposed face of pile 
is about 0.8 X 20 mm. The deflections were as rapid as for a 
bolometer, and its stationary temperature was reached in less 
time than the single swing of the galvanometer needle. In other 
words, its heat capacity was so small that it gave an accurate 
register of the energy falling upon it. In another experiment, 
using a galvanometer sensitiveness of 1 = 5x10"*® amperes, and 
the scale at i meter, i mm deflection = 2?2 x lo"'. The sen- 
sitiveness is the same as that of the best bolometers yet con- 
structed, while its simplicity commends itself even in spectrum 
radiation work. 

The general experience in this country, however, has been that 
the commercial instrument does not fulfill all the excellent quali- 
ties claimed for the one originally described. The wires are 
heavier than in the original specifications, which makes the 
instrument sluggish. 

The problem in thermopile construction is to secm^e a low 
resistance (equal to that of the galvanometer) , a low heat capacity 

'^Rnbens, Zs. fur Instrumentenkunde, 18, p 65; 1898. 

" If /> = the thermoelectric power in microvolts per degree (=53 microvolts for 
iron and constantan), n = number of junctions exposed and r = the internal resist- 
ance, of the thermopile; and if we combine the pile with a galvanometer, which, with 
an internal resistance of w ohms, gives a deflection of tn millimeters per microampere, 
then a deflection of i mm indicates a change in temperature of the junctions of Jt 
degrees where 

npni 



CobU$ttz.] 



Instruments and Methods of Radiometry, 



399 



and heat conductivity, and . a high thermoelectric power. The 
latter requirement is fulfilled by using junctions of iron and 
constantan. The heat capacity can be reduced by using finer 
wire, say 0.06 to 0.08 mm diameter, and by making the unexposed 
junctions smaller than the ones to be exposed. The junctions are 
soldered with quite large beads of silver, which are then flattened 
to present a large surface. The unexposed junctions do not need 
this, and the small bead formed by the fusion of^he two wires 
(with a bit of silver solder if necessary) can be hammered thin, in 
order to have it radiate rapidly. By using finer wires (to reduce 
heat conduction) the resistance will be increased if the dimensions 
of the Rubens pile be retained. In the commercial instrument, 






• • 



• • 



-• •- 



• • 



• • 



4=i: 



-• •- 






♦-•- 



•-•- 



♦-#- 



t 







-•-^ 



•-•- 



-•-♦i 



Fig. 1. 

at least one-third of the wire is between the unexposed junctions 
and the binding posts. The greater part of this wire may be 
eliminated by making the supporting frame narrower, while still 
retaining the original distance between the exposed and the 
unexposed junctions. The elimination of this superfluous wire 
will reduce the resistance by about one-third. In Fig. i is 
shown the original design, a, and the suggested improved design 6. 
In Fig. ic, is shown, on an enlarged scale, a thermopile for "point *' 
sources. By using iron and constantan wires 0.06 to 0.08 mm 
diameter it is p)ossible to place quite a number of junctions within 
a small area. The combination could be used to advantage in a 
F^ry pyrometer, and for measuring radiation from sim spots, 



400 Bulletin of the Bureau of Standards. [yoi.4,No.s- 

etc., in which the bolometer, on account of the smallness of the 
exposed surface, is lacking in sensitiveness. By properly arrang- 
ing the groups, of four or more jimctions each, the combination 
will take the form of a hollow enclosure, which would tend to make 
it a more complete absorber of radiant energy. 

1. Comparison of Old and New Form of Thermopile. — In order 
to test these conclusions in regard to the use of finer wire, a 
new iron-constantan pile of 20 junctions, made of wire 0.08 mm 
diameter, was ordered from the makers of the original instrument. 
Although the specifications were not completely fulfilled (the 
frame was nearly the same size as the original, which increased 
the resistance to 9 ohms) , the sensitiveness was i .4 times that of 
the old type, which has a resistance of 4.8 ohms (wire about 0.15 
mm). By means of suitable switches the two thermopiles were 
connected to the same galvanometer, having a full p)eriod of 12 
seconds (2 = 2 x 10"" amperes) and exposed to the radiation 
from a Nemst heater. For all deflections, as large as 35 cm, the 
new thermopile showed no drift greater than ±2 mm, which may 
be attributed to the galvanometer. On the other hand, the zero 
of the old thermopile would drift 0.5 cm in a 10 cm deflection 
to 2.2 cm in a 27 cm deflection, and it would require 15 to 20 
seconds for the deflection to become zero. 

The two instruments were then tested in a vacuum. The 
sensitiveness of the old instrument was increased only 15 per cent, 
while no change in sensitiveness could be detected in the new 
one, although two distinct tests were made on different days, the 
pressure having been reduced to o.oi mm. The thermopiles are 
moimted on ivory frames and covered with a sheet of copper, one 
side having a slit the other a funnel-shaped opening (i X 15 mm). 
The slit was covered and the radiation passed through the fimnel. 
The whole was suspended from a rubber cork in a wide-mouthed 
bottle, which was exhausted with a mercury or a Geryk pump. 
The source of energy was an incandescent lamp. With 200 ohms 
in series with the galvanometer the deflections were about 10 cm. 
The fact that the sensitiveness of these thermopiles did not 
increase appreciably in a vacuum is rather remarkable. Brandes " 



^ Brandes, Physikal. Zs., 6, p. 503; 1905. 



CoblenU.] 



Instruments and Methods of Radionietry, 



401 



found that a single junction of 0.02 mm wire became 18 times 
more sensitive in a vacuum. Lebedew ** found that a 0.025 mm 
iron and constantan junction, when black, was 7 times, and when 
bright was 25 times, more sensitive at a pressure of o.oi mm than 
at atmospheric pressure. 

Since writing the above an investigation of Moll " has appeared, 
in which he used a modified form of Rubens thermopile. The 
iron-constantan wires were 0.06 mm diameter, the junctions were 
0.2 mm diameter, while the resistance was 12 ohms. The gal- 
vanometer sensibility was /= i X io~' amperes (not very sensitive), 
and had a full period of 12 seconds. The radiation curves were 









\ 










■ 




• 










,* 




'. 






•• 




• 


, 








•i '/*••. 




.' 


.v.... 


1 








OD 


• 


/ H,0\ 








• 


g 


.' 


' 2 • 
• 1 




*% 




H,0 


P 


• 


." /•' *• 




\ 




"V. 




.' 


.".o . 




s 






It. 




• 




••• ' • 




ttl 





















• *'*'• 
















H,0 








f / - 


, 












co,\ 


OOa w.-- 


•'v.. 










•., 


y 




'••^•'•... 


• 




i^-^— •'*• 








H 





0.7 1.4 1.9 2.7 4.3 6 6.5 

Fig. 2. — Energy curve of Nemst Glower, {MolL) 



8fi 



recorded automatically by a device that also registered the zero 
of the instrument after each deflection. The curves must there- 
fore be free from any personal bias, and one is reproduced in Fig. 2 
to show that the thermopile of fine (.06 to .08 mm) wire deserves 
more consideration than it has heretofore received. 

2. The Peltier Effect.— The result of the Peltier effect is to 
lower the temperature of the exposed jtmction. Consequently, 
the thermopile does not give an accurate record of the energy 

" Lebedew, Ann. der Phys. (4)9, p. 209; 1902. 

** W. J H. Moll, Dissertation, Utrecht. February, 1907. 



402 Bulletin of the Bureau of Standards, IV01.4.S0.3 

received. The actual error introduced has never been determined. 
Since there is a possibility of using the thermopile for quantitative 
work in place of the bolometer, it is desirable to learn the degree 
of accuracy of this instrument. 

The rate of generation of heat by the Peltier effect is propor- 
tional to the current, while the generation of heat on account of 
resistance is proportional to the square of the current. Jahn " 
has shown that the heat generated by the Peltier effect, deter- 
mined experimentally, agrees, within experimental error, with 
the value computed from the observed thermoelectric power. 
The value for iron-constantan has never been determined experi- 
mentally*'* but from the work of Jahn it is permissible to compute 
the heat generated in the thermopile by using the known thermo- 
electric power, which is about 50 X 10"' volts. 

Using a galvanometer of 5 ohms resistance and having a figure 
of merit of ^' = 3 X io"'° amperes per mm for a scale at i m, and 
an iron-constantan thermopile of 20 junctions, wire 0.08 mm and 
5 ohms resistance (see footnote 1 2) ; 

I mm = 2 X 10"* degree. 
The Peltier effect in calories is computed from the formula: 

p ^ Tii dE 
" / ~dt 
where T = 274°, i = 3 X io~^* c.g.s. units, t = 5 seconds, / = 
4.2 X io~^ and dE/dt = 50 X 10"' c.g.s. units, 

.*. P = =b5 X io~** gr.-cal. (in 5 seconds). 
The total weight of the junctions is about o.oi gr. and the specific 
heat is about 0.1 gr.-cal. 

Hence the temperature change of the exposed junctions is: 

Jt = —^ — - = 5 X 10"" degree (for i mm deflection) 
0.1 X o.oi 

and since the temperature of the unexposed junctions is changed 

an equal amount in the opposite direction the total change 

Jt = I X io~" degree. But a deflection of i mm = 2 X lo""* 

^« Jahn, Wied. Ann., 84, p. 755; 1898. . 

'®" Since writing this it has been found that Lecher, Ber. Akad. Wiss. Wien., Ho, 
p 1505, 1906; Sci. Abstracts, 1083, 1907, has recently determined this constant to 
be 12.24 gr.-cal. per amp.-hr., while the value previously computed was 10.5 gr-ca]. 
per amp.-hr 



cobienu,] Instrujnents and Methods of Radiojuctry, 403 

degree, hence the error is i part in 200 under the best theoretical 
conditions. In practice the temperature sensitiveness will not 
be so great; it will be shown presently to be of the order 5 X lo"' 
degree, whence the Peltier effect would cause an error of i part 
in 500, or I mm in 50 cm, which is as close as one can read such 
large deflections. Since the Joule heat depends upon the square 
of the current, it is negligible. Further consideration of the 
thermopile as an instrument for quantitative measurements will 
be found below in connection with the bolometer. 

It will be noticed presently, that prior to his construction of 
the iron-constant an thermopile, Rubens used several very sen- 
sitive bolometers, all of which were displaced by the thermo- 
pile. For exploring spectra with very narrow lines, the linear 
bolometer is probably better adapted than the pile which, how- 
ever, may be covered with a diaphragm, having a narrow slit. 
For extreme sensitiveness it equals the bolometer, and it is a 
noteworthy fact that all the investigations in the extreme infra- 
red and ultra-violet parts of the spectrum, where the energy is 
weak, have been accomplished by means of the thermopile. 
Unless one can build up an elaborate bolometric apparatus in a 
room not exposed to direct sunlight, the thermopile will give the 
more reliable readings, as far as the constancy of the zero is con- 
cerned. Whether or not the thermopile will give a true measure 
of the energy falling upon it will depend upon the manner in 
which it is employed. It requires no particular skill to manip- 
ulate, and is easier to protect against temperature changes than 
is a bolometer with its storage battery. The older form of 
thermopile used by Melloni, Tyndall, and others were subject to 
drift similar to that observed with the bolometer. This was not 
due to unequal increments of resistance, as in the bolometer, but 
to thermoelectric effects at the binding screws, to the connecting 
wires moving in the earth's magnetic field, and principally to 
the large heat capacity gf the junctions. Most of these disturb- 
ances, however, are small and easily avoided in the Rubens type 
of thermopile. Since the bolometer strips and the balancing 
coils are of dissimilar material, it is also subject to thermoelectric 
disturbances. 



404 Bulletin of the Bureau of Standards. \voi. 4,^0.3. 

V. THE RADIOMETER. 

The manner in which an interesting scientific toy can be made 
to serve a useful purpose is well exemplified in the radiometer 
of Crookes," discovered about 1875. By fastening bits of pith 
(the one black, the other white) at the ends of a long straw, which 
was suspended by means of a silk fiber in a long glass tube, he 
was able to make measurements of radiant energy, even at that 
early date. Pringsheim*' simplified the instrument somewhat, 
suspended the vanes bifilarly with silk thread, and used it to 
investigate the infra-red spectrum of the sun, produced by means 
of a glass prism, to about i .5/i. From this the first really useful 
radiometer was developed by Nichols. *• 

It consists of two similar thin vanes of blackened mica or 
platinum attached to a horizontal arm, and suspended in a 
vacuum by means of a fine quartz fiber. The vanes are about 
3 mm from the window. The radiation to be measured falls 
upon one of the vanes, which becomes slightly warmed. This 
causes the residual gas molecules to rebound with increased 
velocity from the blackened surface, and the reaction pushes the 
vane from the window. There is a small mirror attached to the 
glass staff which supports the vanes, and the deflection is ob- 
served by means of a telescope and scale. At certain gas pres- 
sures the exposed vane is attracted toward the window instead 
of being repelled from it. The behavior of the radiometer has 
been worked out theoretically by Maxwell *° in his paper on 
"Stresses in Rarefied Gases Arising from Inequalities of Tem- 
perature.*' Among other things, he showed, that for two par- 
allel disks very near each other the central points will produce 
but little effect, because between the disks the temperature 
varies uniformly, and only near the edges will there be any stress 
arising from an inequality of temperature in the gas. It has 
been shown by others, especially by Crookes and by Nichols, that 
the sensitiveness of the radiometer is i function of the pressure 
of the residual gas, of the kind of gas surrounding the vanes, and 

»^ Crookes, PhU. Tmns. (II), 106, p. 325; 1876. 

** Pringsheim, Ann. der Phys. (3), 18, p. 32; 1883. 

*• Nichols, Phys. Rev., 4, p. 297; 1897. Ber. der Beriiner Akad., p. 1183; 1896. 

2° Maxwell, Collected Papers, 2, p. 681. Phil. Trans., Part I, 1879. 



Cobitniz.\ 



Instruments and Methods of Radioynetry, 



405 



of the distance of the exposed vanes from the window. The 
latter, on account of its absorption, limits the region of the 
spectrum that can be investigated. If the vanes are not too 
close to the window, the deflections will be proportional to the 
energy falling upon one of them. 

1. Comparison of Sensitiveness and Area of Vane. — For vanes 
of small dimensions, such as must be used in practical work, the 
writer has found that the deflections are proportional to the area 
of the exposed surface of the vane. This is perhaps to be expected, 
although there seemed to be some doubt. The curve, Fig. 3, of 



cm 
20 



























y 


y 
























y 


y 




,y 


^ 




















y 


y 


y 


y 




















^-^ 


Y 






y 




















f 




H 


y' 




















y 


y 


y 


t^ 




















^ 


y 


,^ 


y^ 






















/ 




^ 


y 






















./ 


> 


X' 


























/^ 




WIOT 


H OF 1 


•XP08 


iD VA 


4E 



















14 



z12 
O 

S10 



.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 mm 

Fig. 3. — Variation of Radiometer deflections with area exposed. 

deflections and exposed area of vanes (area 10.5 x 1.3 mm for 
constant pressure of 0.02 mm) does not pass through the origin. 
One explanation may be that for infinitely narrow vanes the 
graph is not a straight line, but curves as it approaches the origin. 
Because of the impracticability of suspending vanes of different 
widths successively from the same fiber suspension, at the same 
distance from the window, and using the same gas presstu-e for all 
vanes, it was necessary to use one wide vane, with a slit before it, 
and vary the opening of the slit. The sotu-ce of energy (Nemst 



4o6 Bulletin of the Bureau of Standards, IV01.4.N0.3. 

heater) was at a distance of 3 meters, and hence the width of the 
projection of the slit up)on the vane was practically the width of 
the slit, except for a very narrow slit when diffraction may 
decrease somewhat the energy incident on the vane. This, 
however, would displace the graph still farther from the origfin. 
The forces acting in a radiometer are so complex and so little 
understood that no further examination was made to ascertain 
the limits within which the above proportionality holds. The 
test of proportionality was made to reduce the deflections to unit 
area between the above limits of exposed vane. It is of interest 
to note in this connection that in a bolometer the sensitiveness 
varies as the square root of the area of the bolometer strip. 

In his earlier communications the writer held to the belief that 
the weight of the vanes and their size were the most important 
factors in determining the sensitiveness and period of a radiometer. 
However, so many factors enter into the problem that it is difficult 
to decide this point, and the following test may be of interest, 
showing that the diameter of the quartz fiber suspension is an 
important factor in determining the sensitiveness. 

2. Comparison of Sensitiveness and Diameter of Fiber Suspen- 
sion. — Using the same vanes (0.5 x 9 mm area) the sensitiveness 
and period were foimd for a heavy and a light quartz fiber suspen- 
sion. The main difficulty was to insure that the vanes were at 
the same distance from the window, and that the pressure was the 
same in the two cases. Hence these quantities are only approxi- 
mate. In Table II it will be noticed that in changing from a 
heavy to a light fiber the sensitiveness is increased 4.5 times, while 
the period was increased almost three fold. It further shows that 
for the same (light) fiber the sensitiveness was doubled (36 to 7 1 cm 
per mm) by changing the presstu-e and the distance from the 
window, which was of fluorite and hence opaque beyond 10 ft. 
The sensitiveness of 71 cm per mm* of exposed area is the highest 
on record. This, however, was not the maximum sensitiveness, 
since the pressure was 0.02 mm, while radiometers have their 
maximum sensitiveness at a pressure of about 0.05 to o.i mm. 
At this pressure, however, heat conduction would cause annoyance. 
The vanes of this suspension were of platinum foil o.oi mm thick, 
covered on one side electrolytically with platinum black and then 



Coiieniz.] Instruments and Methods of Radiometry. 407 

smoked over a candle. It is best to cool the gases from the flame 
by placing a wire gauze, or sheet of metal full of holes, between 
the flame and the vanes when smoking them. These vanes were 
suspended by means of one of the finest workable quartz fibers, 
and when within 3 mm of the window either one of the vanes 
would always approach and adhere to it, even at atmospheric 
pressure. From tests with fluorite windows, which from internal 
strains might be piezoelectric, and with rock salt windows when 
bare and also when covered with tinfoil, it was foimd that this 
efltect is not due to electrification. Starting with the vanes 
parallel and at a distance of about 5 mm from the window it was 
found that, as this distance was decreased, one of the vanes 
(generally the one to be exposed to radiation) would approach 
the window, and for a distance of about 3 mm would turn imtil 
the plane of the vanes was at right angles to the window. The 
observations extended over several months, and all evidence 
indicates that this effect is due to gravitational attraction. As a 
result of this the deflection of such a vane would not be proportional 
to the energy received. This radiometer had no torsion head to 
control the zero. However, for general work with very sensitive 
radiometers a torsion head would be necessary since the best 
pumps may leak, which will cause a slow drift. It will be shown 
presently that this is about 5 times the sensitiveness of Snow's 
bolometer, for which i mm deflection (scale at 3 m) indicated 
a temperature difference of 7?6 x lo""*. In other words, this 
radiometer would detect -^-^-^^ -^-^-^ degree rise in temperature. 
But the period of the radiometer was 6 times that of the bolometer- 
galvanometer, which is its weakest point in radiation work 
requiring a short period. 

A comparison can also be made (Table II) between hght vanes 
(0.5 X 9 mm) and heavy ones (1.3 X 10.5 mm) at the same pressure 
but having different quartz fiber suspensions. The results show 
that while the hght vanes are more sensitive than the heavy ones 
(see Table III), there seems to be no hmit to the sensitiveness 
attainable in either case, without considering the period. The 
idea of not considering period of vibration with sensitiveness 
seems reasonable, for by sensitiveness is meant the minutest 
15298—08 5 



4o8 



Bulletin of the Bureau of Standards. 



\V€i,4.N9 3> 



quantity of radiation one can detect, assuming one is willing to 
wait long enough for the deflection to reach a maximum. In 
Table III are compiled the most notable radiometers used in 
radiation work. The candle as a standard of comparison is not 
ideal, but since the sensitiveness of the various instruments varies 

TABLE II. 
Sensitiveness of Radiometers. 



Deflection 
per mm* 




Remarks 



Vanes (area 0.5X9, mm wei^t 5 mg) 3 : 

from window. 
Vanes closer to window. 



Same yanes (0.5X9 mm), finer qnartz fiber. 



Pressure 



Pull Period 



0.02 mm 
0.03 " 



0.04 



2 min. 
2.5 '» 



Deflection 
per mm* 



36 cm 
71 " 



Remarks 



63.5 



Vanes 3 mm from window candle at 3 m. 

Vanes nearer window. This is the greatest 
recorded sensitireness. A deflection of 1 
mm on scale at 1 m = 2?5 X 10~*. 





Heavy vanes, area 1.3X10.5 mm, weight lO+mg. 


0.02 mm 


40 sees. 


5.5 cm 


Distance of vanes from window miknown. 


.02 " 


60to64 " 


13.7 " 


1 Vanes nearer window, hence longer period. 


.026 " 


36 to 40 " 


8.5 " 


Vanes farther from window than in preceding. 


.035 " 


25 *' 


3.3 " 


1 Vanes still farther from window, which 

shortens period and decreases sensitiveness. 

1 For a pressure of about 0.05 mm the sensi- 

1 tiveness would be much greater. 

1 



by a factor from 2 to 20, it is sufficiently accurate for the present 
comparison. In this table it will be noticed that for the same 
period the various radiometers vary in sensitiveness by as much 
as 50 per cent. Porter's radiometer was the most sensitive of 
the instruments having a period of 90 seconds. But he gained little 
on the whole, for the vanes were so light that he could work only 



Coblemlg.] 



Instruments and Methods of Radiometry. 



409 



during; quiet hours at night. On the other hand, the writer, after 
trying light vanes, adopted heavy ones," and was thus enabled 
to continue his observations at all hours without annoyance even 
from a large air compressor which was situated in an adjoining 
basement room. 

TABLE III. 

Sensitiveness of Various Radiometers. 



Observer 



Pull period 



Area of vanes 
mm' 



Deflections per mm* 
area of exposed 
vane; candle and 
scale each at i m 



B.F. NicholB 

PhjB. Rev., 4, p. 297, 1897. 

Astrophys. Jonr., 18, p. 101, 1901. 
Stewart 

Phys. Rey., 18, p. 257, 1901. 
Drew •. 

Phys. Rey., 17, p. 321, 1903. 
Porter 

Aetrophys. Jonr., 22, p. 229, 1905. 
Coblentz 

Abe. Spectra 

Phys. Rey., 16, 20, and 22. (Vac. 

tube.) 

Another yane 

(Thia Bulletin, ibid.) 



12 

11 " 
80 " 
5 min. 
901 



90 

90 
50 

100 
150 

70 



2X15 

3.1 
30 

7 

3.6 

15(10X1.5) 
12 

11(11X1) 
4.5 



cm(?) 



u 
u 
u 



12.5 
4.9 
17 
17.1 

27.5 



8 to 10 " 
10 to 12 " 



52 

71 

35 



tt 



3. Sensitiveness Compared with Wave-Length of Exciting 
Source. — In his investigations of emission spectra of the alkali 
metals, using a prism and lenses of quartz, and a bolometer, Snow" 
found that the vapor of the carbon arc had the larger portion of 
its energy concentrated in one large band in the violet. The 
writer using a radiometer, a rock-salt prism, and a mirror spec- 
trometer for investigating infra-red emission spectra, found that 
the radiometer gave small, if any, deflections in the violet. The 
violet band is far enough from the reflection minimum of silver 

21 *« Investigations of Infra-red Spectra; " 1905. 
" Snow, Phys. Rev., 1, pp. 28 and 221; 1893. 



4IO Bulletin of the Bureau of Standards. [Voi.4.1^0.3, 

not to be weakened by it, hence it appeared that the radiometer 
might be selective in its behavior to radiant energy. 

To test this point the following experiment was tried: The 
total radiation from the aluminum spark (with glass-plate con- 
denser) on a 10,000 volt transformer was measiu'ed with a very 
sensitive radiometer (p)eriod 65 to 70 seconds, sensitiveness 35 cm 
per mm') just described, and with a bolometer to be described 
subsequently. The window of the radiometer was of white 
fluorite 2 mm thick, hence transparent to the ultra-violet, but 
opaque beyond lo/i. A large part of the energy of the altuninum 
spark hes in the ultra-violet. The maximum energy of the warm 
electrodes occurs at about 8/i. The radiation from the spark 
passed through a quartz cell 8 mm thick, containing distilled 
water which absorbed the infra-red energy. The observations 
consisted in obtaining the ratio of energy transmitted by a glass 
plate 8 mm thick (which is opaque to rays shorter than 0.3 m)> to 
the total energy of the spark. 

Unfortunately at the high sensitiveness required for meastuing 
ultra-violet radiation the two instruments were not in perfect 
working order at the same time. During the first test the bolom- 
eter-galvanometer had a short period — 10 seconds — and catised 
trouble by the drifting of the zero with changes in the spark, 
while in the second test the radiometer was leaking slightly, which 
caused its zero to drift. Then too the spark was by no means 
constant, but, as will be seen presently, the ratio above referred to 
is about the same for the radiometer and the bolometer, after 
correcting for the loss of 4 per cent by reflection at the fluorite 
window. The agreement is close enough to show that the radiom- 
eter is not selective in its action, and hence is adapted to investi- 
gations in the ultra-violet. 

In the first test the direct radiation from the aluminum spark 
(with a condenser in parallel) was compared with the part trans- 
mitted by glass. There was some infra-red energy in this case, 
which made the ratio lower than in the second experiment. The 
direct deflections with the radiometer were about 20 cm. The 
ratio of the deflection through plate glass to the direct deflection 
varied from 17 to 19.5 per cent (mean about 18 per cent), while 
with the bolometer the same ratio varied from 16 to 20 per cent. 



cobienu,] Instruments and Methods of Radiometry. 411 

the mean being about 19 per cent. The bolometer followed the 
fluctuations of the spark, hence the greater variations. The 
spark was 75 cm from the radiometer and 25 cm from the bolom- 
eter. • In the second test the infra-red radiation was absorbed 
by the cell of water, with quartz windows. Plate glass was again 
used to absorb the ultra-violet. In this test the average ratio of 
the radiation transmitted by the glass to the total radiation was 
about 65 per cent, while the same ratio for the bolometer was 67 
per cent. Correcting for the loss by reflection at the window, the 
ratio for the radiometer would be about 69 to 70 per cent. 

The results as a whole show that the radiometer is not selective, 
i. e., it is as efficient in the ultra-violet as is the bolometer. 

4. The Radiometer Compared with the Bolometer. — In dis- 
cussing the merits of the radiometer writers have generally 
emphasized the fact that it is not adapted for quantitative work, 
since it can not be caUbrated. As a matter of fact, in reviewing 
the work done in radiation it was found that even with the bol- 
ometer there are only a few cases where the energy was obtained 
in absolute measure. Even in the study of the laws of radiation 
from a hollow enclosure, or Kirchhoff radiator (so-called "black- 
body"), the galvanometer deflections were observed and reduced 
to a single standard of sensitiveness, which was in arbitrary units. 
The same can be done with the radiometer. Its sensitiveness is 
easier to control, since it can be made to depend only upon the 
pressure of the residual gas; whereas the constant of a galva- 
nometer varies continually. It is not affected by magnetic varia- 
tions, and a heavy vane is less affected by earth tremors than is a 
very light galvanometer suspension. It is sensitive to temper- 
ature changes, but less so than the bolometer, and it can be more 
easily shielded from temperature changes than can a bolometer 
with its galvanometer, battery, etc. The fact that it is not 
portable is not a serious drawback, since it is not usually neces- 
sary to move the instrument. It has two disadvantages, viz, 
its window, or preferably double window, is selective in its trans- 
mission, and its period is somewhat longer than that of a bolom- 
eter and galvanometer of equal sensitiveness. But the latter 
is nearly always drifting and to repeat one's readings takes as long 
for an observation as it does with a radiometer. Since the 



412 Bulletin of the Bureau of Standards. \_voi. /, No. 3. 

weight is of minor importance, tremors are avoided by having 
the suspension weigh about 8 to 10 mg. When used with a good 
merciuy pump it requires no attention after it is adjusted. A 
delicate galvanometer requires frequent adjustment and, in con- 
nection with a bolometer, the investigator's time is occupied 
principally with the care of the instrument (at least that has been 
the writer's experience) , which should be a secondary matter. 
The two instruments are of the same order of sensitiveness, with 
the possibility of the radiometer being the more sensitive. This 
is well illustrated in the test for their efficiency to ultra-violet radi- 
ation, where both instruments were at about their maximum work- 
ing sensitiveness. The bolometer used was 0.22 X 10 mm in area, 
resistance 2.8 ohms, and for a bolometer current of 0.04 ampere, 
with a galvanometer sensitiveness of i = 1.5X10"*® ampere (full 
period = 16 seconds), had a temperature sensitiveness of 9® X io~' 
per mm deflection, on a scale at i m. (See Table IV.) A candle " 
at I m gave a deflection of 45 cm, which, on the assumption that 
the sensitiveness is proportional to the square root of the area of 
bolometer strip, is 30 cm per mm*. For the radiometer, having 
a vane 0.5 X 9 mm, a candle gave a deflection equivalent to 1 59 cm 
at I m, or, since the deflection is proportional to the area of the 
exposed vane, 35 cm per mm' (Table IV) . In other words, the 
radiometer was 1.2 times as sensitive as the bolometer, or i mm 
deflection corresponded to 7?5 X io~*. (For a full period of 2.5 
minutes its sensitiveness was 3?8Xio"*.) Its period, however, 
was 4.5 times that of the bolometer-galvanometer. This exami- 
nation of sensitiveness is based on the assumption that the radi- 
ometer was as complete an absorber of energy as the bolometer. 
Judging from its period, its efficiency is much lower than that of a 
bolometer, hence the radiometer must be sensitive to temperature 
changes less than the value just given. 

The sensitiveness of bolometers thus far attained is about 
T TTTriwTj degree per mm deflection. Paschen (loc. cit.) claims a 
sensitiveness of TTTTrA-TTTTr degree by reading to o.i mm. But 
the conditions are rare when one can read to o.i mm, so that the 
estimate would seem too high. As will be seen presently, the 

2* A Nernst-heater was also used in making the comparison. 



cobuntg,] Instruments and Methods of Radiometry. 413 

working sensitiveness is of the order of t i^^f tttttt degree, or even 
considerably less. The maximum sensitiveness is of course needed 
only in cases where the radiation is very weak. 

5, Some Points in Radiometer Construction. — There is room 
for great improvement in radiometer construction. One must 
expect some difficulties in controlling instruments of great sen- 
sitiveness. There are always inequalities in the two sets of 
junctions of a thermopile, so that when it is first connected to a 
very sensitive galvanometer, the deflection must be brought back 
to its original point by adjusting the control magnets. The same 
is true of the very sensitive radiometers constructed by the 
writer." On exhausting the instrument the deflection will move 
off the scale (deflection away from the window) and must be 
brought back by means of a torsion head. If the pump leaks 
there will be a drift toward the window. The deflection seems to 
be due to the inequality of the temperature of the window and 
the metal shield, back of which is the vane that remains unexposed. 

By placing the vanes at a greater distance, 6 to 8 mm, from the 
window, in the sensitive radiometer just described, it was found 
that the drift due to sudden changes in the temperature of the 
window was avoided and a torsion head was not needed. The 
use of a torsion head has been found necessary only in the most 
sensitive radiometer (deflection = 50 cm per mm*) . The drifting 
of the zero is a far less serious matter than in a bolometer or a 
thermopile, and is not troublesome in less sensitive instruments. 

The dimensions to be chosen for the vane will depend on its 
distance from the spectrometer slit. The image of the sUt can 
be made to just cover the vane by placing a short focus (say 10 to 
12 cm) condensing mirror between the spectrometer slit and the 
radiometer vane. Since mica vanes are not opaque to all rays, and 
since the lampblack may rub off, it is better to use platinum 
vanes, about 0.0 1 mm thick, blackened electrolytically and then 
smoked. 

In addition to having the radiometer enclosed in a heavy metal 
case to shield it from temperature changes, it is advisable to 
cover the instrument with a metal cylinder and to pack wool 
between it and the inner case. In warm weather it has been 
found that the vanes become easily electrified from the mercury 



414 



Bulletin of the Bureau of Standards. [roi. ^, .\o.j. 




i_l_JL_i' 



Fig. 4. — Radiometer. 



A k. 



cobieniz.] htsiruments and Methods of Radiometry, 415 

vapor. This is avoided by placing gold foil on cotton between 
the pump and the radiometer. This electrification effect is not 
well understood. It seems to be most noticeable when a fluorite 
window is used next to the vane. This does not always seem to be 
true, however, for in the ultra-violet radiation test just described 
there was but one window, with the metal slit on the outside and 
the vane inside, and no difficulty was experienced with electrifi- 
cation. Without disturbing the vane, a second fluorite window 
was placed inside the first one, hoping thas to avoid heat conduction. 
After several days' trial it was foimd impossible to prevent the 
vanes from being attracted to the inner window, even when 
covered with tin foil, and it was necessary to replace this window 
by rock salt. It is well known that plates of fluorite after being 
cut from a crystal are frequently under internal stresses; but 
whether this could produce sufficient polarity, as in the case of 
quartz, is not known. The freedom from electrification with rock 
salt may be explained on the assumption that it is hydroscopic 
and dissipates any electrical charges on its surface. 

In spectrum energy work the best method of varying the sensi- 
tiveness of a radiometer is to use a sectored disk of variable 
aperture. The sensitiveness may also be varied by turning the 
leveling screw, which is in line with the windows vj. w. in Fig. 4. 
The complete instrument is here shown, except the bulb containing 
gold foil on cotton. The figure is drawn to scale and needs but 
little explanation. The outer metal shield, c, is shown dotted. 
Between it and the heavy metal case is wool or hair felt. The 
double windows of rock salt or fluorite are shown at w. w. The 
torsion head, /, is self-explanatory, as is also the vane which is 
also drawn to scale. The viewing window, b, of glass, for adjusting 
the vane on the slit, as well as the glass window, a, for viewing the 
scale, are fastened permanently with melted shellac or ** Khotin- 
sky '* cement. The joints at the top and at the rock salt window, 
fe, fe, are made with a mixture of beeswax and tallow, and painted 
with shellac, which has been found to make air-tight connection. 

VI. THE BOLOMETER WITH ITS AUXILIARY GALVANOMETER. 

We have now to consider one of the most useful radiation 
meters yet devised, namely, the bolometer, which is simply a 



4 1 6 Bulletin of the Bureau of Standards. [ v<a, 4, J^'o. 3 

Wheatstone bridge, two arms of which are made of very thin 
blackened metal strips of high electrical resistance and high 
temperature coefficient, one or both of which are exposed to 
radiation. When thus exposed their temperature changes, thus 
unbalancing the bridge, and the resulting deflection of the gal- 
vanometer gives a measure of the energy absorbed. The maxi- 
mum sensitiveness of the bolometer is limited by the size of the 
strip to be exposed to radiation. Any further gain in sensitive- 
ness must be attained by increasing the sensitiveness of the galva- 
nometer, which, for the moving magnet type varies approximately 
as the square of its period (undamped). The sensitiveness is 
also directly proportional to the bolometer current, but this is 
limited by the resistance of the bolometer strips. It will be 
noticed presently that the working sensitiveness of the various 
galvanometers thus far used is of the order of 2 x 10"*® ampere 
per mm deflection, while the working temperature sensitiveness 
of the bolometer and galvanometer varies from 5 x 10"* degree 
to 5 X 10"" degree for i mm deflection. 

!• Historical Summary. — The various types of bolometer-gal- 
vanometer apparatus will first be noticed, in so far as they relate 
to spectro-radiometric work. 

The first great step in improving the moving magnet galva- 
nometer is due to Kelvin, who decreased the weight of the moving 
parts to a few milligrams, and introduced the astatic system of 
magnets. 

The main problem in bolometer construction is to use strips 
of a metal having a high resistance-temperatiu-e coeflicient, a 
small specific heat, and a low-heat conductivity. Such metals are 
nickel, platinum, tin, and iron, but, for various reasons in mechan- 
ical construction, platinum is the most commonly used. The 
manner in which this instrument was developed to its present 
high sensitiveness is best illustrated by considering the various 
designs of different investigators. 

The pioneers in exact spectro-bolometric work are Langley, 
Angstrom, and Julius. While I^angley was not really the first 
to discover the principle of the bolometer, he was the first to 



cobi€ntx.\ Instruments and Methods of Radiome try. 417 

invent a practical instrument'* and demonstrate its superiority 
to all other radiation meters for accuracy, quickness of action, 
and adaptability. His improvements of the instrument extend 
over a long period, and it will be sufficient to say that whereas 
his first instrument had a temperature sensitiveness of o?ooo 02 
per mm deflection of the galvanometer, the latest recorded a 
temperature change of o?ooo 001 per mm deflection, when used 
with a galvanometer having a figure of merit of i = 5 X lo"^** 
arai>ere. For his solar radiation work the bolometer strips are 
about 12 mm long, 0.05 to 0.2 mm wide, and have a resistance of 
about 4 ohms. The wire is obtained as '*Wollaston wire" of 
0.1 mm diameter inclosing a platinum core of 0.0125 mm. This 
is flattened by hammering, after which the silver is dissolved in 
nitric acid. He found that a thickness of less than 0.002 mm 
is inadvisable, thinner ones being disturbed mechanically by air 
currents. The current used was about 0.03 ampere. The galva- 
nometer generally used at the Astrophysical Observatory has 
1.6 ohms resistance. The bolometer strips are of platinum, while 
the balancing resistances are of platenoid, which is practically 
the same as German silver. It was finally found that the maxi- 
mum sensitiveness " of the bolometer circuit is closely approx- 
imated when the balancing coils are upwards of 4 times the resist- 
ance of the bolometer strips, and the galvanometer resistance is 
not less than 0.6 or more than 4 times the resistance of the bolom- 
eter strip. The bolometer strips, balancing coils, and slide 
wire adjustment are all enclosed in a double- walled chamber, 
which eliminates accidental drift of the galvanometer needle. 
The whole outfit is in a room which can be maintained at a 
constant temperature. This has reduced the drift to a minimum. 
The published details of some of the more important bolom- 
eters and accessory apparatus used in radiometric investigations 
are summarized in the following table (Table IV): 

*Langley, Proc. Amer. Acad., 16, p. 342; 1881. Chemical News, 48, p. 6; 1881* 
British Assoc. Report, 1894, (o?oooooi) Annals. Astrophys. Obs., 1. 
''Abbot, Astrophys. Jour., 18, p. i; 1903. 



4r8 



Bulletin of the Bureau of Standards. 

TABLE IV. 
Bolometer-Gralvanometer Sensitiveness. 



{yoL4,No.3. 





Galvanometer 


Bolometer 














E 









■ 






• 








■ ^ 






a 




• 




« c 






.s 


Observer 


1 


8 


8| 


1 




11 







■ 


♦3^ 









a 


B 


?'g 


a 






..* 




d<a 






U l» 




s 


\ 


V M 


1 


% 
E 

I 


r 




« 


9 




V 






Oi 


% 


o 


^ 


< 


<a 


Lan£ley. 






lto5xlo-io 


4 


0.05tD0.02 


0.03 


AxuuQsAstrophyB. Ota. 










Xl2 




Abbot. 


1.6 


20 


5X10-W 








AstropbyB.J.^lS, p. i; 1903. 














Angstrttin. 














WiM. Ann., 26, p. 253; 1885. 














WiM. Ann., 86, p. 715; 1889. 










0.1X12 




WiM. Ann., 48, p. 497; 1893. 


8 


16 


5.7xlO-« 


5 






Julius. 














LichtundWInneetraUang, p. 31; 1890. 


2.7 




4xl0-« 


3 


0.3X14 


0.133 


Bdmbifltz. 






8xlO-» 


8.8 






Verb. PbyB. GeseUach., Beilin, 7, p. 














71; 1888. 














Lummer and Kulbaom. 














Zb. fQrlnstnunentenknnde, 12, p. 81; 






1.5X10-* 


60 


12X1X32 


0.006 


1892. 














Wied. Ann.,46,p. 204; 1892. 














Rubens. 














Wied. Ann., 87, p. 255; 1889. 


5 


4tD5 


3.2X10-W 


5.2 


7X0.3X35 


0.2 


Wied. Ann., 45, p. 238; 1892. 


80 




3.2X10-W 


3 


3X0.2X10 






80 




3.2X10-W 


80 


0.09X12 





CoUeHtx.] Insiruments and Methods of Radiometry. 

TABLE IV (continued). 
Bolometer-Galvanometer Sensitiveness. 



419 



Temperature BeneitlveneBe 



li 

Si 



•C. 
1X10-* 



9xl0-» 



8X10-B 



3xl0-« 



2X10-^ 
5xl0-« 

8xlO-« 



1 

■ 

i 



2.5xlO-» 
4XlO-» 



8S 



«2a 



%' 



4X10-* 



Candle test 



s 

I 



f 



1 



I 



aoo 



1 - 

«« 5 o 

a s-a 



5 
2.7 



Remarks 



In pnctioe for a6lar spectnun work a foil period 

of 3 MC8. and i»2.2xlO-» ampere is used. 

Balancing ooDa of platinoid. B<doineter is 

endosed in water Jacket. 
In pFBCtioe drifting is minimfg^ by placing a 

short copper wire in series with one of the 



Sufaoe bdometer; 23 strips of tin foU; black- 
ened with Pt dt and soot. Balancing coils 
of copper wire in separate box. SensitlTe- 
ness 556 X io-» gr-cals/cms/sec. 

Single Pt strip 0.1x12 mm in spectnrtNdometer. 

Two aims of tin foil in ftem of grating. Sensi- 
tiyeaees also given as i27xio~* gr- csls/cm* 
sec. 

Bolometer strips of nickel 0.002 mm. thick. 
Balancing ooOs of platinnm wire in oil in 
separate box. Found deflection proportioinal 
to current. 

Suxfaoe b(dameter, four similar aims, so no 
compensating resistances needed; diagonally 
opposite aims exposed. Sensitiyeaees also 
t^yen as 533 x io-» gr-€als/cm>/sec. 

Sorfiuw b(dameter, four similar arms of pilati- 
nam fbil o.ooi mm thick; two diagonally 
opposite aims exposed to radiation; the sur- 
face consists of 12 strips of platinum, 1 mm 
wideX32 mm long, separated by 1.5 mm, 
back of which openings are 12 similar strips 
of the diagonally opposite arm. Bolometer 
cunents as high as 0.04 ampere could be used. 

Surface bOtometer of tin foil 0.01 mm thick; 
7 strips in each arm. 

Two aims of 0.04 mm iron wire hammered flat; 
three strips in each arm. 

Two aims of 0.005 mm platinum wire ham- 
mered flat. 

The deflections of the galvanometer were pro- 
portional to the current through the bolometer 
and the rise in temperature of the aims propor- 
tional to the incident energy. 



420 



Bulletin of the Bureau of Standards. 
TABLE IV— Continued. 



\Voi,4.No.3, 



Observer 



Gftlvanometsr 



I 
s. 



I 

t:6 



S 



6 



E 



E 



Rnbens and finow. 

Wtod. Ann., 46, p. 529; 1892. 



Pliyt. R07., 1, p. 31; 1893. 



WIM. Ann., 55, p. 401; 1895. 

DODAth. 

WiM. Ann., 58, p. 609; 1896. 



Wtod. Ann., 48, p. 272; 1893. 



W. W. C. 



ISO 
140 



20 



5.2 
5.2 



1.8X10-" 
1.5X10-W 



6x10-" 



6x10-" 



2.3X10-" 
3.3x10-" 



1.6x10-" 
8.3X10-" 



13 



0.09x12 ! 
0.05x7 0.025 



0.04 



0.01 to 0.02 



3x0.5x15 0.03 I 
0.25x7 .02 i 



2,5x10-10 
1.5xlO->o 2.8 



0.22x10 0.04 



RnbenB Thermopito. 
W. W. C. Rndiometer. 



5 ' 

1 


14 
70 
150 


1.4x10-10 


1 
1 3.5 

j 


0.8X20 
0.5x9 
0.5x9 



codienu.] Instrumenis and Methods o/Radiomeiry. 

TABLE IV— Continued. 



421 





Candle tMt 




8- 

81 


8 

M 


!l 


a 

« 


1 


.s 


it 




u 


1 

• 


\ 


ll 


Ig 


ill 

1^^ 


Remarks 


M g 


1 






I1 







3xlO-« 










40 




For Hefner candle at 1 m. 


8xlO-« 


2.4xl0-» 


4x10-4 


1 


3 


15 


8.3 


Two btdometeraims of pUtinun O.ooo 936 mm 
thick; iMUandng coils of Geiman sOTor; 4 
coU galvanometer, total of 7200 tuna , woond 
with two siaee of wire. Xacnet eyitem of 
12 macnetB 3 to 4 mm long; total weight of 
ejratemsomg. 


3X10-* 


1.2X10-* 






4 
3 






Two bOlometar anna of 3 iron wliee hammered 
flat. 

Two anna of pUtinnm 0.17 mm wide x 0.0074 
mm thick; balancing ooila (of pUtlnum) of 
elaborate design in sepaiate box. Drifting 
waaserioos. 

Bolometer anna of platinvm o.ooi to 0.0005 mm 
thick. 

Oompensation resistances of mawgsnin wire, 
final adjustment on pUtinnm wire with 
mercury contact. 


lxlO-« 


2.7xlO-« 


iixio-* 




2.7 






•Galvanometer; 4 ooOs 40 mm external and 5 


»4xlO-» 


2.1X10-* 


8x10-* 




2.5 






mm intonal diameter, 1,200 tanis of graded 
wire in each coH; moving system, 13 mag- 








1 






nets in each gioap, 1 to 1.5 mm long, on 
















both sides of glass stalf, and 0.3 mm apart; 
















minor 2 mm diameter x 0.03 mm thick. 
















Total weight of system =:S mg. 














Using an »-magnet system and a fan period of 




9xl0-« 9xl0-« 


1 


1 


45 


30 


20 sees. 1=^8X10-" ampere, while a fr-mag- 












net system had a sentibDity of i-2.5xi0-» 




1 1 






ampere for a full period of 36 seconds. 


i.ixio-« 




lXlO-« ' 5 


(1?) 


10 15 




7.5X10^ 


,2.3 


1 30 


35 


fTheee values are obtained by comparing the 


3.8xl&-*t! 3 

1 


1 ! 35.5 


71 


' deflections per unit area with the bolometer. 



422 Bulletin of the Bureau of Standards. \voi, 4.^0,3, 

IvUmmer and Kurlbaiim *' improved the design of the surface 
bolometer by using thin platinum foil (0.00 1 mm. thick) and 
making the arms of high resistance by a special grid construction, 
by selecting four arms of as nearly the same resistance and temper- 
ature coefficient as possible, and by exposing two diagonally 
opposite arms to the radiation. Snow'* was among the first to 
give much attention to the possible gain in sensibility by the use 
of a more sensitive galvanometer. Paschen " continued the work 
in this direction and constructed the most sensitive galvanometer 
used up to that time. By the use of very light magnet systems 
and a long working period (as much as 30 sees.) a marked increase 
in sensibility was attained. He adds that for a full period of 40 
seconds and a battery current of 0.06 ampere through his bolom- 
eter, by reading to o.i mm, it would have been possible to de- 
tect o?ooo 000 I . However, such a long period and large battery 
current is not practicable, so that the last estimate of temperature 
change has little meaning. Even for a full period of 20 seconds 
the magnetic and thermal disturbances are generally sufficient to 
interfere with bolometric work, and a fair estimate of the sensi- 
tiveness attained by Paschen is T-(r^ J-TnrTr degree for a scale at 3 m. 
In the Astrophys. Join-., 3, p. 24, 1896, he gives a practical example 
of the sensitiveness of his bolometer. The complete period of 
his galvanometer was 34 seconds and for a scale at 2,5 m the 
sensitiveness was i — 8.3 X 10"" ampere. With a cmrent of 0.02 
ampere through the bolometer (dimensions = 0.25X0.0005 mm; 
resistance = 8 ohms) , a deflection of i mm corresponded to a diflFer- 
ence in temperature of 84° X IO"^ or 2?i X 10"* for a scale at i m. 
This sensitiveness was attained in the present work for a very 
much shorter period but higher cmrent. Paschen appears to have 
been the first to use manganin wire in his balancing coils and a 
heavy platinum wire with a mercury contact for the final compen- 
sation, all of which were in a separate wooden box. 

From this historical record it will be noticed that a fair estimate 
of the temperature sensitiveness of the various instnmients is 
about 5° X lo"" for i mm deflection on a scale at a distance of i m. 

^Zs. ftir Instnimentenkunde, 12, p. 81; 1892. Wied. Ann., 46, p. 204; 1892. 
*Phys. Review, 1, p. 31; 1893. 
*> Wied. Ann., 48, p. 272; 1893. 



coduniz.] histruments and Methods of Radiometry. 423 

Most instruments cited fall far below this value; but the cases are 
exceptional where so great a sensitiveness is needed. For measur- 
ing radiation at low temperatures, or for vacuum tubes, or for the 
examination of the remote ends of the spectrum this great sensi- 
tiveness is required. It is a significant fact that the bolometer 
with its long period galvanometer has not been used for such work. 
Here the Rubens thermopile is the most serviceable and reliable. 

Mendenhall and Waidner'* constructed a sensitive galvanom- 
eter of 4 coils, having an external diameter of 15 mm, internal 
diameter 2 mm, wound with six sizes of wire, 500 tiuns in each coil. 
The resistance (with coils in parallel) was 3 ohms. They used 
3 magnets in each group, lengths = 1.15 nun, total weight of 
suspension system i mg, and attained a sensitiveness of 1 = 5.6 X 
lo"" ampere for a full period of 9 seconds and scale at 2 meters 
distance, or i . i x 10"*® ampere at i meter. 

Abbot*' built a 16 coil instrument which had a resistance of 1.6 
ohms. The sensitiveness wasi=5 Xio"" ampere for a complete 
period of 20 seconds and scale at i meter. However, to increase 
the steadiness of the needle for solar-energy spectra the full period 
is reduced to only 3 seconds. Assuming that the deflection is 
inversely proportional to the square of the time of single swing 
(true only for low air pressures) the sensitiveness is i = 2.2 X io~" 
ampere for a full period of 3 seconds. 

IngersoU*^ has recently constructed a sensitive galvanometer 
similar to the one described by Mendenhall and Waidner (loc. cit.) . 
The galvanometer has 4 coils of 20 ohms each, 16 mm outside and 
2 mm inside diameter; weight of suspended system less than 2 mg. 
The highest sensitiveness attained was 4 X 10"" ampere for 5 ohms 
resistance and scale at 1.5 m, but lack of steadiness and propor- 
tionality of deflection led him to reduce the sensitiveness to 2 X 10"" 
ampere per mm deflection with a 10 second period for ordinary 
usage. His bolometer was 0.5 X 8 mm, and at highest sensitive- 
ness a candle at i m gave a deflection of 200 cm on the galvanom- 
eter scale at a distance of 1.5 meters. His balancing coils are of 
"lA" wire, which is practically the same composition as '*con- 

•* Mendenhall and Waidner, Amer. Jour. Sci., 27, p. 249; 1901. 
** Abbot, Astrophys. Jour., 18, p. i ; 1903. 
" IngersoU, Phil. Mag. (6), 11, p. 41 ; 1906. 
15298—08 6 



424 Bulleim of the Bureau of Standards. [Voi. 4,^0.3. 

stantan** or ** advance" and hence, like German silver or plate- 
noid, is subject to thermoelectric disturbances. 

2. The Construction of Sensitive Galvanometers. — One of the 
best known sensitive galvanometers on the market is the du Bois- 
Rubens'* type. This instrument is magnetically shielded by 
enclosing the coils within two spherical shells of iron. There are 
two coils of about 6 cm external diameter. Two magnet systems 
are furnished with the galvanometer. The heavy system, which 
has a large mirror, has 14 magnets about 7 mm long arranged on 
both sides of an aluminum staff. The lighter one has 10 magnets 
about 4 mm long. The galvanometer tested by the writer was 
found to give deflections proportional to cmrent for deflections 
as large as 30 cm, which is often an important item. The large 
weight of the moving system is of some importance in places where 
there are severe mechanical disturbances. In this galvanometer 
with the two coils in parallel, resistance = 2.85 ohms, using the 
complete magnetic shield and the heavy system of magnets, the 
sensitiveness was i = 4 x 10"*® ampere for a full period of 6 seconds 
and circular scale at i meter. Using the light system and a 
full period of 6 seconds, the sensitiveness was onlyi = 7 x 10"' 
ampere, even after it was remagnetized. But in both cases, and 
especially with the light system, the zero kept shifting back and 
forth continuously, so that its maximum working sensitiveness 
was limited to this value. On the other hand, the galvanometer 
with short magnets, to be described presently, shielded with only 
one cylinder of iron, situated close beside the du Bois-Rubens 
galvanometer and tested at the same time, had a perfectly steady 
zero, even for three times this period, when its sensitiveness was 
i= 1.5 + 10"*^ ampere. In the latter instrument, however, the 
coils are small and the proportionality between cmrent and 
deflections does not hold for deflections greater than 10 to 12 cm; 
but, since a shunt must be provided anyway, the deflection can 
be kept within these limits so that this is not a serious objection. 
A four-coil galvanometer, also due to du Bois and Rubens,'* which 
has been much used abroad, may be obtained on the market. 

^* Du Bois and Rubens, Ann. d. Phys. (4) 2, p. 84; 1900. 
3* Du Bois and Rubens, Wied. Ann., 48, p. 236; 1893. 



cobuniz.] Inslrumenls and Methods of Radiomelry, 425 

This is a much larger instrument, of the Thomson astatic type, 
than the one described above and is not adapted to magnetic 
shielding. The instrument is furnished with two sets of four coils, 
of 20 ohms and 2000 ohms each, respectively, and three magnet 
systems of 1500, 250, and 100 mg, respectively. 

In this country the type of small-coil galvanometer just men- 
tioned is being very generally adopted, although it is not to be 
obtained in the market. The question of the best form of coils, 
size of wire, kind of magnets, etc., has been thoroughly discussed 
by Mendenhall and Waidner,®* and by Abbot," so that little 
need be said on that subject. However, the manner of assembling 
the different parts into a small space for convenience in magnetic 
shielding and at the same time leaving the suspended system 
open to view (but shielded from air currents) seemed to admit of 
further improvement. The following design of an easily shielded 
galvanometer is the result of a study of previous types, and while 
it can not claim any new principles, the simplifications may 
appeal to the reader. Further simplifications are possible by 
changing the position of the binding posts to the base of the 
instrument, when the shield of Swedish iron (Fig. 6) can be 
brought closer to the coils. I^abor in construction may be saved 
by imbedding the coils in paraffin instead of mounting them on 
insulated supports. Since the proximity of the upper and lower 
pairs of coils increases the deflection of the needle, they should be 
close together, and the control magnets should be on a long rod 
extending above or below the coils. 

(a) Form of Coils, — The proper form and method of winding 
galvanometer coils to seciu-e a maximum effect from a given 
weight or resistance of copper has been thoroughly discussed by 
Maxwell.** He shows that the greatest effect is obtained by 
winding the coil with different sizes of wire, beginning with the 
smallest size, and by winding each layer so that it lies within the 
surface the polar equation of which is r' = d* sin fl, where r is 
the length of the radius making an angle 6 with the axis of the 

^Mendenhall and Waidner, Amer. Jour. Sci., 12, p. 249; 1901. 

*' Abbot, Astrophysical Jour., 18, p. i, 1903. Annals Astrophys. Obs., 1, p. 246, etc. 

^Maxwell, Electricity and Magnetism, II, p. 360. 



426 Bulletin of the Bureau of Standards, \ voi, ^. No. j. 

coil, and d the value of r when 6 = 90°. Abbot (loc. cit.) has 
computed the most efficient coils satisfying these conditions, and 
gives a large table of results for coils wound with a single wire 
and for coils wound with three sections of wire of diflFerent diam- 
eters. He found that the total force exerted at the center is closely 
proportional to the 0.45 power of the total resistance and that 
coils composed of three sections of best sizes of wire give about i .4 
times the force of a coil of the best single size of wire of the same 
total resistance. In his best 25-ohm coil, wound in three sections, 
the diameters of the wires are 0.08, 0.16, and 0.32 mm (B and S 
size 40, 34, and 28). The lengths are 256, 1031, and 4144 cm, 
respectively, while the external diameter of the complete coil is 
3.3 cm. 

In the present design the coils (20 ohms each) were computed 
for three sections of B and S gauge, Nos. 40, 36, and 30 wire, but 
were finally constructed of Nos. 40, 36, and 32, diameter of wire 
0.07, 0.127, and 0.199 mm, and lengths 1.9, 4.1, and 12.3 m, 
respectively. The external diameter of the coils is 18 mm, the 
internal diameter 2 mm. The wire was covered with a single 
layer of white silk insulation. 

The mandrel described by others for winding the coils did not 
prove strong enough and a new one was devised. It is given full 
size in Fig. 5 ; the, dotted^ lines indicate the method of winding 
the sections. To prevent the wires from slipping it is necessary 
to apply a dilute solution of shellac while winding. To make 
the coils rigid they are boiled in camauba wax imtil the air bubbles 
are all expelled.'*® Some of the shellac will come out in boiling. 
After the coil has cooled the nut is taken oflF and the plate of the 
mandrel is warmed and removed. On warming the heavy metal 
end of the mandrel the coil drops off. However, there is a tend- 
ency for the shellac to adhere to the plate and to the cone of the 
mandrel, and it is well to cover these parts with a thin layer of 
camauba wax or paraffin before winding the coil. In winding 
the coils the ends of all the sections are brought out and soldered 

3«»By accident the lines are drawn full instead of broken ones. 

^ This wax has a high coefficient of expansion and cracks on cooling, so that the 
writer prefers refined paraffin, which i^ easier to work and there is less likelihood of 
charring the silk insulation. 



CoblenU.] 



Instruments and Methods of Radiotnetry. 



427 



-B- 



"U" 




SIDE VIEW OF A 



W~^^ 


( i 


v..,y 


,fe"""^'; 


K°) 


* 35-mni ► 





I I i ! 



O 



"U" 



u 



± 



5cm 



Fig. 5. — Cabfonometer. (In the mandrel the curves should be dotted, ) 



428 Bulletin of the Bureau of Standards, \voi, 4, no.j. 

together (in series) at the back of the coil. It is important to 
use pure copper wire covered with a single layer of white silk. 
To avoid static charges of electricity it is customary to cover the 
coil faces with tin foil or gold leaf. A free space of at least a 
millimeter between the coil faces is necessary. (See Nichols, 
" The Galvanometer. ' 

(6) The Needle System, — The best dimensions and construction of 
the needle system has been extensively investigated by Paschen, by 
Mendenhall and Waidner, and by Abbot. In any magnet system 
the greatest sensibility is attained when the ratio of the magnetic 
moment to the moment of inertia of the system is a maximum. 
For two systems of magnets otherwise equal, if the magnets of 
one are n times shorter than the other then its moments of inertia 
is n' times smaller than the other. The result is that the one 
with the shorter magnets will give n* times the deflection of the 
first,*° if the two systems be astaticised to the same period. How- 
ever, Mendenhall and Waidner (loc. cit.) have shown that it is 
possible to use too short magnets. In their graphs of sensitive- 
ness and length of magnets there is a decided maximtun for a 
length of I.I mm. It has been found that magnets about i to 
1.2 mm long, 0.2 mm wide, and 0.08 to o.i mm thick are very 
efficient. 

During the course of the present investigation it was suggested 
that a more sensitive instrument would be produced (irrespective 
of period) by using a suspended system composed of many mag- 
nets. A system was constructed containing 20 magnets (10 in 
each group, 5 on each side of the staflF) of the same size and kind 
of material as a lo-magnet system (5 magnets in each group) 
previously employed. This system, although made with the 
greatest care; proved to be far less satisfactory than those having 
less magnets. It was foimd that it made but little difference 
whether the system was composed of 6 (weight 5 mg), 10, or 20 
(weight 10 mg) magnets, and, as will be noticed in the references 
just quoted, this appears to be the general experience; that is to 
say, one can deduce theoretically the best proportions for the 
magnet system, but their realization is limited by mechanical 

^ If the magnetic moment of the magnets varied directly as their length, which is not 
the case. 



cod/en/z.] . Instnimefits and Methods of Radiometry, 429 

difficulties. Of course, in the heavier systems the period will be 
longer for a given sensitiveness; but the better the astaticism the 
higher the attainable working sensitiveness, while the fewer the 
magnets the easier it is to get them into the same plane. This is 
most easily done by fastening them in place with a sugar solution 
on a piece of ground plate glass on which the dimensions of the 
system are marked in pencil. The glass staff is then attached by 
means of shellac, which is allowed to dry (touch with a hot wire) , 
when the system is loosened from the glass by means of hot water. 
The system is magnetized in a double electro-magnet in the form 
of a C 13 the intensity of magnetization being 1000 to 2000 lines 
per cm*. 

In the present experiment the magnets were made from a bar 
of timgsten steel, which was cut into thin sections of about 0.008 X 
1X2 cm. These thin plates were then cut into strips o.i to 0.2 
mm wide, and hardened, glass hard, by heating them to a red 
heat on an iron plate and plimging them into water. Although 
they were not tempered afterwards, they showed no marked 
change in astaticism on standing for several months. The 
lengths of the magnets were from i.o to 1.2 mm. The mirror 
was of thin microscope cover glass about 1.5 X 2 mm. 

Astaticising the system is apparently a simple operation, but 
in practice it is foimd otherwise. The system is suspended in a 
glass tube and by means of a magnet of known polarity it is 
determined which group in the system is the stronger. The 
latter is then weakened by bringing a like pole (use a weak magnet 
or a steel knitting needle) near it. In the same manner the weaker 
group of magnets is strengthened by bringing a strong imlike 
pole near to it. It is quite impossible to make the two sets of 
magnets so perfect that their planes will be parallel, so that in 
astaticising the two sets of magnets will be of equal strength 
when the system points east and west. The complete period 
may then be as long as 6 to 10 seconds, although the latter is 
rarely attainable with such light systems. Since the magnets 
are mounted with shellac, which is hydroscopic, it is possible that 
the change in astaticism is due to a variation in humidity. This 
might be avoided by using refined paraffin in moimting the mag- 
nets. The finest quartz fiber must be used, viz, such that the 



430 Bulletin of the Bureau of Standards, ivoi.4,no.3. 

suspension head may be turned through several revolutions with- 
out deflecting the astaticised needle by more than a few scale 
divisions. 

(c) The Assembled Galvanometer, — The galvanometer without the 
shields is drawn to scale in figures 5 and 6, and needs but little 
explanation. The side, Ay is adjustable for admitting the magnet 
system. The coils are fastened to the ebonite supports by means 
of soft wax (a mixture of Venice turpentine and beeswax which 
hardens on standing). This permits an easy adjustment of the 
faces of the four coils to paralleUsm by simply inseting a piece 
of plate or microscope glass between them. The coils are then 
made vertical by means of the tripod screws. The needle system, 
shown at right angles to the coils, is then centered by tilting 
the tube, B, which is held to the frame by means of a screw, and 
can be lifted off at will. The top, C, can also be removed for 
moimting the fiber. The sides of the galvanometer are covered 
with microscope section glass, secured by soft wax. This prevents 
disturbances due to air currents, and at the same time admits 
excellent illumination of the interior. The ebonite supports and 
the binding posts may be omitted entirely by way of further 
simplifications. The coils are then moimted in paraffin, which 
provides the insulation. 

{d) Sensitiveness of Galvanometer, — Using the lo-magnet system 
(weight about 5 mg) , 5 magnets in each group, separated 0.4 mm, 
with the mirror between the coils, the sensitiveness for a full 
period of 9 to 10 seconds was i = 2.5 X 10"^® ampere, and for a 
full period of 18 seconds i = 1.5 X 10"^® ampere, the scale being 
at I meter. The sensitiveness of the 20 magnet system was only 
i = 3 X io"^° ampere for a full period of 20 seconds, while an 
8-magnet system (4 in each group) had a sensitiveness of i = 
8.9 X 10"" ampere per mm deflection for the same period, 20 
seconds. A light, 6-magnet system had a sensitiveness of i = 
2.5 X 10"" ampere for a full period of 36 seconds. The de- 
flection was aperiodic (i. e., there was only one turning point) 
for a full period greater than 8 seconds. The resistance for the 
four coils in parallel was 5.23 ohms at 20°. 

This is not the highest attainable working sensitiveness, since 
the faces of the coils were separated about 2.5 mm to avoid the 



co^kniz.] Instruments and Methods of Radiometry, 



431 



effects of static charges which may be troublesome in a newly 
moimted suspension. However, after the magnetic shields were 
in place and the instnunent was adjusted, it was not disturbed 
in order to make the final test. By placing the mirror above or 
below the coils, and thus bringing the upper and lower pair of 
coils closer together (i mm is about the limit) a greater sensitive- 
ness would (theoretically) 
have been possible. In a 
subsequent test, however, it 
was found that bringing the 
upper and lower pairs of 
coils closer together had but 
little if any effect in increas- 
ing the sensibility. In fact 
a high sensibility, for a given 
period, depends more upon 
the lightness and the perfec- 
tion of the needle system. 
The glass (or quartz, which, 
however, is more brittle) 
staff must be straight, to 
avoid an increase in the mo- 
ment of inertia of the sus- 
pension system. Menden- 
hall and Waidner (loc. cit.) 
show that for a badly con- 
structed system, in which 
the axis of rotation departs 
0.2 mm from the staff at its 
upper extremity, the sensi- 
bility will be decreased by 
25 per cent. By using a gal- 
vanometer having small coils the glass staff will be short and 
easily drawn straight, while the complete system will be light. 
The glass rod may be straightened, after being drawn, by suspend- 
ing it with a weight at one end, and heating it with a gas flame, 
or by simply heating a heavy glass rod until it is melted, and 
permitting one end to draw out the fiber by means of gravity. 




5 cm 



Fig. 6. — Galvanometer with inner magnetic shield. 



432 Bulletin of the Bureau of Standards, \yoi, 4.^0.3- 

Where there are serious mechanical disturbances it is advantageous 
to use heavy systems. Since such disturbances are often encotm- 
tered and elaborate galvanometer supports have to be provided, 
it may be noted that frequently the disturbance (tremors) is local, 
and that by selecting a diflferent part of the same room the ill 
effects may be avoided. As a practiced example the present 
galvanometer was very unsteady on a massive wall bracket; but 
by placing the galvanometer on a heavy box in the same place 
upon this bracket, the tremors were entirely eliminated. 

The sensitiveness of a galvanometer (undamped) is approxi- 
mately proportional to the square of the period. In the present 
tests the sensitiveness was found to be quite approximately pro- 
portional to the period, due to the air damping of the light magnet 
systems. 

{e) Proportionaiity of Galvanometer Deflections. — It is desirable 
to have the proportionality of the galvanometer deflections to hold 
throughout a long range, and an attempt was made to attain 
this end. 

From the various sizes of galvanometer coils mentioned in which 
about the same sensitiveness was attained, irrespective of the size 
of the coil, the writer concluded to use coils larger than 2 cm 
diameter, e. g., 3 cm to 4 cm diameter, in which the proportionality 
of cturent to galvanometer deflections ought to hold for deflections 
as large as 15 to 18 cm. The magnets would be the same length, 
I to 1.2 mm, as in the small coils (cf. Paschen, who used coils 4 cm 
diameter, magnets 1.5 mm long, and found the proportionality to 
hold for large deflections). To test this conclusion two additional 
galvanometers, having coils of 6 and 20 ohms, respectively, were 
constructed. The 6-ohm coils were wound with three layers of 2 
ohms each, using B and S gauge Nos. 38, 30, and 26 wire, 
single covered white silk insulation, diameter of bare wire 
o.ioi, 0.255,0.405 mm, lengths 92, 595, and 1375 cm, respec- 
tively. The complete coil was 2.8 cm diameter and 7 mm through 
its thickest part. The 20-ohm coils were wotmd in three sections of 
equal resistance using B and S gauge Nos. 40, 34, and 28, diameters 
of wire 0.080, 0.160, and 0.321 mm, lengths 190, 770, and 3080 cm, 
respectively, and were 3.2 cm in diameter. Using B and S gauge 



CodiemU.] 



Instruments and Methods of Radiometry. 



433 



Nos. 38, 34, and 30, lengths 310, 770, and 2000 cm, a coil 2.6 cm 
diameter is produced. 

The relations between the cmrents through the galvanometers 
and the corresponding deflections are shown in Fig. 7. Curve a, 
for the small coil (four 20-ohm coils in parallel, 18 mm diameter, 
magnets i mm long) galvanometer shows that the deflections are 



em 














y 


/ 




/ 


90 












/ 


/ 


/ 


/ 




!»25 

i 

10 








J, 


/ 


f 


/ 


/ 










i 


V 


d 


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»ERE 



10 2080406060 70 8090 lOOl 
Fig. 7. — Proportionality of Galvanometer Deflections, 

proportional to the current up to about 8 cm. Using a lo magnet 
system (magnets 1.4 mm long), curve 6, the proportionality of 
deflections with current holds for values as large as 16 to 20 cm, 
depending upon the sensitiveness, which in this case was about 
2Xio~** ampere. The proportionality is of course greater for 
the less sensitive instrtunent. 



434 Bulletin of the Bureau of Standards, \voi. 4. N0.3. 

The deflections observed when using the 6-ohm coils (four coils 
in parallel) were proportional to the current up to 30 cm. This 
is the only instrument tried in which the period was affected by 
varying external resistance, which indicates that in the other gal- 
vanometers the damping is due to the air. 

Curve c gives the deflections for the 20 ohm, 32 mm diameter 
coils (in parallel) , with a system of 1 2 magnets (6 at each end) i .6 
to 1.8 mm long. Here the proportionality holds for deflections 
as large as 30 cm. The magnet system weighed about 8 mg 
which reduced the sensitiveness to 3.5 X 10"^** ampere for a full 
period of 12 seconds. 

Of all these galvanometers, in which about a dozen different 
styles of magnet systems were used, the one having the smallest 
coils (18 mm diameter) proved the most satisfactory except for 
proportionaUty. As has just been shown, by a judicious selec- 
tion of longer galvanometer magnets, the proportionality of deflec- 
tions with current may be made to hold true for large deflections 
with but slight loss in sensitiveness for a given period. 

(/) Magnetic shielding. — In places where the magnetic field is sub-v 
jected to great variations it is necessary to surroimd the galvanom- 
eter with an iron shield, which is most efficient when it is in the 
form of spherical or cylindrical shells of different thicknesses**^ of 
iron. For convenience in working, it is desirable to have the sys- 
tem of shields occupy a small space, which necessitates the use 
of metal shells of small diameter. This is a desirable feature 
for efficiency in shielding, but, since the shells usually become 
permanent magnets in handling, there is great difficulty in length- 
ening the period of the galvanometer needle. It is therefore a 
matter of trial in placing the control magnets in such a position 
that they weaken the combined fields of the shields. In fact, it 
was found easier to place a short magnet (steel file) so that it 
controlled the suspended system and then weaken its field thati to 
overcome the complex field of the shields, by means of the control 
magnets. 

^°» Wills, Phys. Rev. 24, p. 243, 1907, finds that for both spherical and cylindrical 
systems the best conditions are obtained when the radii of the shells are in geomet- 
rical progression. 



cobientz.] Instruments and Methods of Radiometry, 435 

For magnetically shielding the small coil galvanometer used in 
this work four sections of annealed soft steel pipe, about 30 cm 
long, diameter 7, 10, 15, and 20 cm, respectively, and 4 to 6 mm 
thick, were provided. In practice only the two middle tubes 
were used, the inner one being discarded on account of the unusual 
difficulty experienced in controlling the galvanometer, as just ex- 
plained. 

The mirror was viewed through slits i cm high cut into the 
shields. Although this is supposed to produce an asymmetrical 
field it made no appreciable difference, since the slits were far be- 
low the coils. An inner shield was made from Swedish iron (Fig. 6) , 
which had a circular hole, bored vertically to admit the suspended 
system and the coils, which were mounted in paraffin. This inner 
magnetic shield was found to be superior to the others just de- 
scribed, since it is easier to anneal and does not become a perma- 
nent magnet in handling. The shield with the glass windows, 
w, Wy serves as a further protection against air currents. By taking 
the leads out through the bottom of the galvanometer, they will 
pot interfere with the outer shields. In the present work the 
Swedish iron proved as efficient as the system of soft-steel pipes 
and no outer shields were provided. 

It is customary to provide a symmetrical pair of control mag- 
nets (30 to 40 cm above the coils) placed upon a contrivance 
which permits an independent horizontal rotation and a vertical 
motion.*' This is desirable in work extending over a long time, 
for the astaticism of the needle system is constantly changing, 
which requires a frequent adjustment of the control magnets in 
order to keep a fairly constant galvanometer period. 

3. The Construction of Sensitive Bolometers. — In the bolometer 
the sensitiveness is closely proportional to the square root of the 
surface, so that in spectnun energy work, where the bolometer 
strip is narrow, the sensitiveness attainable through the bolometer 
is limited. 

The general complaint against the bolometer is its drift, which 
is of two kinds, viz, (i) a slow shift of the zero scale reading due 
to an unequal change in resistance in the bolometer strips and 

*^ See Wiedemanns "Electricitat." 



436 Bulletin of the Bureau of Standards, \voi,4. ^'0,3. 

(2) a fluctuation of the readings due to air currents and magnetic 
perturbations. This ought to be the most pronounced for bolom- 
eters having large surfaces, although some writers are of the 
opinion that the narrow strip bolometer is subject to the greatest 
variations from mechanical vibrations and air currents. There 
are so many possible sources of trouble in a bolometric outfit that 
it may be worth while to notice them, (i) The auxiliary gal- 
vanometer is subject to magnetic perturbations, and, if exposed 
to great temperature changes, its sensitiveness is changed, due 
to a variation in the resistance of the coils. The sensitiveness 
and zero reading is also constantly changing, due to variations in 
the magnetic field. (2) The bolometer strip is affected by air 
drafts and, if very thin, by mechanical vibrations. (3) The 
electric circuits are subject to temperature (resistance) changes 
which vary the bolometer current. (4) The storage-battery cur- 
rent is irregular, due to changes in temperature and to polarization. 
The gases surrounding the bolometer may affect the reading. 
Lummer and Pringsheim " found that variations in the amount of 
moisture in the air changed the sensitiveness of the bolometer. 

If, therefore, one is working in a well-lighted (southern expo- 
sure) and well-ventilated room, a drift is to be expected. As an 
illustration of this, Abbot (loc. cit.) found **that the difference of 
radiating power between an observer's black coat, distant 2 m 
from the balanced bolometer, and the walls of the room which 
his coat momentarily hid, threw the spot of light off the scale some 
40 cm, while the observer's naked hand within a meter of the bo- 
lometer turned the galvanometer needle roimd and round.*' The 
writer found that his balanced bolometer (not in use for observa- 
tions, however) would not shift i mm in half a day when it was 
cloudy, but on bright days, with every passing cloud, or on windy 
days the scale readings would fluctuate back and forth through 
several centimeters. It is therefore advisable to work in a base- 
ment room located on the north side of a building. In this connec- 
tion it may be noticed that the radiometer is more self-contained, 
and all its parts are concentrated in a small space in which it is 
easier to control the temperature. The same is true of the 
thermopile. 

*2 Lummer and Pringsheim, Ann. der Phys. (3) 68, p. 398, 1897. 



codienu.] Instnmients and Methods o/Radiometry, 437 

(a) Best Resistance of Bolometer and Balancing Coils. — In all 
the bolometers that have been used by foreign investigators the 
four arms were chosen of equal resistance. Lummer and Kurl- 
baum *^ consider the bolometer a simple Wheatstone bridge which 
is at its maximum sensitiveness when the four arms and the 
galvanometer are of equal resistance, and the e. m. f. is constant. 
In reality we vary the e. m. f.; and Reid** has shown that con- 
sequently the resistance of the balancing coils should be consider- 
ably larger than that of the bolometer. Child and Stewart" have 
shown experimentally that the sensitiveness is increased by having 
the resistance of the balancing coils several times that of the 
bolometer strips. Abbot" has also shown that the maximum 
sensibility is very nearly attained when the balancing coils are 
upward of four times the resistance of the bolometer strips, and 
the galvanometer resistance is not less than 0.6 or more than four 
times the resistance of the bolometer strip. This has led to the 
general adoption (in America) of a resistance for the compensation 
coils which is from 10 to 20 times that of the bolometer strips. 

The equation *^ showing the relation between bolometer sensi- 
tiveness 5, the bolometer current /, the temperature coefficient, e, 
of the part of the strip exposed, a, the resistance of the bolometer 
strips, r, the absorption coefficient of the surface exposed to radia- 
tion, A , the emissivity of the whole surface, E, the area of the surface, 
F, the heat capacity, W, and the galvanometer constant, k, is: 

From this it will be noticed that the sensitiveness is increased 
by decreasing the heat capacity and the emissivity; and by 
increasing the bolometer current, the temperature coefficient, the 
resistance, the absorption coefficient, and the surface. Since for 
a given thickness and width of strip the resistance is proportional 
to the surface, it follows from the above equation that the sensi- 
tiveness is proportional to the square root of the exposed surface. 

^ Lummer and Kurlbaum, Wied. Ann., 46, p. 204; 1892. 
^ Reid, Amer. Jour. Sci., 85, p. 160; 1888. 
** Child and Stewart, Phys. Rev., 4, p. 502; 1897. 
^Annals of the Astrophys. Obs., Vol. I. 



438 



Bulletin of the Bureau of Standards, 



[Vol. 4. No. 3. 



The resistance of a wide bolometer may be increased by placing 
several strips side by side. For n such strips in series the resist- 
ance will be increased n times, and for the same cinrent the sensi- 
tiveness will be increased by ^n. If the breadth of one strip is 
increased n times, the current can be increased n times; but since 
the resistance of the strip is reduced n times, the sensitiveness 
remains as before. It follows, therefore, that the greatest sensi- 
tiveness is attainable in a bolometer having a large surface. 
This is well illustrated in the work of Lummer and Kurlbaum ^^ 
who were thus able to use a galvanometer having a sensitiveness 
of only i = 1.5 X lo"* ampere. For the same reasons the sensi- 
tiveness of a linear bolometer 
is very limited, and recoiu^e 
must be had to a sensitive 
galvanometer. 

4. Design of a Bolometer. — 
Langley's bolometer** is the 
only one described in which 
the complete instrument is 
enclosed in a metal case to 
shield it from temperature 
changes and drift. The in- 
strument was intended for 
use in a vacuum, and hence it 
was complicated in construc- 
tion. He used a bridge with 
a sliding metal contact to 
balance the bolometer arms. In the instrument used by the 
writer the friction contact gave so much trouble that a mercury 
contact was devised. The ideas contained in the present design 
were incorporated after an examination of all the important 
bolometers previously described, and hence are not new. The 
instrument as a whole, however, contains simplifications which 
it is hoped may be of use to others. It is possible to place 
the bolometer in a vacuum, but since the sensitiveness attained 





] f ? t y 



Fig. 8. 



^^ Lummer and Kurlbaum, Wied. Ann., 46, p. 208; 1892. 
^* Langley, Annals of the Astrophys. Obs., 1. 



Coblentx.] 



Iiistruments and Methods of Radionietry, 



439 



is not commensurate with the difficulties arising in the use of the 
instrument, no attempt has been made to do so. This form of 
bolometer is of course less portable than the one in which the 
balancing coils are in a separate box, but the cases are rare where 
it is not possible to keep the bolometer stationary and rotate the 
prism table or the other spectrometer arm. 

As above stated, the mechanical difficulties involved in making 
a thin bolometer strip are such that platinum is the best adapted. 
Platinum in silver wire may be hammered or rolled into flat strips. 
In an accurately adjusted jewelers' roll it is possible to press bare 
platinum wire 0.025 mm thick into strips 0.003 mm thick. To 
do this the rolls are screwed together quite tight (not as tight as 
possible as one would suppose) and the wire is passed back and 
forth many times, in the meantime applying heavy lubricating oil, 



n c 



8iDE VIEW 




1 ? M ? <= 



Fig. 9. 

which seems to aid in producing a thin strip. During the oper- 
ation the wire must be annealed frequently. Platintmi in silver 
foil of any desired thickness can now be purchased (Sy and 
Wagner, Berlin), from which strips of any desired width can be cut. 
The strips can be cut acciu'ately to the desired dimensions on a 
dividing engine, but there is danger of tearing the foil unless 
a suitable cutting tool is made. The steel shears shown in Fig. 8 
were constructed for the purpose of cutting strips of the same 
width with a smooth edge, and have proved very serviceable. A 
pair of bolometer strips is cut at one stroke from a double sheet 
of the platinum in silver foil. In this figure, c, is a clamp with 
screws to secure the foil while cutting. The rest of the apparatus 
is self-explanatory. The diflference in the width of a pair of 
strips was found to be of the order of 0.0 1 mm. 
15298—08 7 



440 



Bulletin of the Bureau of Standards, 



[Voi.4,1^'0.3. 



END VIEW 



GALVANOMETER 



To construct a bolometer in which the resistances of the strips 
are equal within i per cent, to have the surfaces as nearly equal 
as possible, and, after this adjustment, to cover these strips 
electrolytically with platinum black and then with soot is a 
difficult operation. In cases where an absolute raeasiu'e of 

radiation is not desired, it is 
unnecessary to use the electro- 
lytic bath, candle smoke being 
sufficient, in which case there 
is but little difficulty in black- 
ening the bolometer. Linear 
bolometers which are less than 
0.00 1 mm thick are torn by the 
surface tension of the electro- 
lytic bath, or the nitric-acid 
bath used in removing the sil- 
ver from the platinum, and are 
extremely difficult to adjust. 
Paschen overcame this difficulty 
in part by stroking the platinum in silver strip (mounted on an 
ebonite holder) with a drop of nitric acid, held in the end of a 
small glass tube, until the silver was dissolved and the two arms 
were of equal resistance. In the present work the silver was 
removed from the strips before 
mounting them.. 

In blackening the bolometer 
strips it was found that the 
resistance would sometimes 
change. The platinum strips 
were, therefore, annealed, before 
mounting, by heating them elec- 
trically, to a red heat, which 
served the additional purpose 




BOLOMETER 
Fig. 10. 




t_L 



3 cm 



Fig. 11. — Hemispherical mirror. 



of burning off a black residue which remains after dissolving the 
silver from the platinum and which is liable to make a poor con- 
tact. In mounting the bolometer strips on the holder, the one 
to be exposed to radiation is first soldered in place. The unex- 
posed strip is made a little longer, so that it will have a slightly 



Cobltmiz.] 



Instruments and Methods of Radiometry, 



441 



greater resistance, which by sub- 
sequent resolderingismadeequal 
to that of the exposed strip. 

The present bolometer con- 
sists of three separate parts, viz, 
the funnel, F, for admitting the 
energy to the bolometer, Fig. 
9, the outer double- walled case, 
C, which may be filled with 
water (running water has a va- 
riable temperatiu-e) , and the 
frame, A , holding the bolometer 
strips, the compensation coils, 
and the balancing wires with 
sliding mercury contact, d, Figs. 
12 and 14. The frame A, Figs. 
9 and 12, can be easily removed 
from the case, which is an im- 
portant factor. The concave 
hemispherical mirror w, Fig. 1 1 , 
is used to reflect back to the 
bolometer strip, 6, Fig. 13, any 
energy which has not been ab- 
sorbed by it. The support and 
adjusting screws for this mirror 
is attached to the bolometer 
frame A, but is not shown in 
these illustrations. 

In Fig. 10 is shown an end 
view of the bolometer, in which 
it will be noticed that the bolom- 
eter strip is adjustable about a 
vertical axis by means of the 
screws, fe, k. The horizontal 
adjustment, /?, is not shown in 
detail. The two pairs of bind- 
ing posts, G and B, connect the 
galvanometer and battery to the bolometer by means of heavy 





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442 



Bulletin of the Bureau of Standards. 



[ Vol. 4, Ao. J. 



twisted copper wire. The frame itself for supporting the screws, 
c, c, Figs. 9 and 12, is composed of three rods, e, e, e, attached 
to two brass plates, A, h. The small telescope, E, is used to 
adjust the bolometer in the spectrum. 

In Fig. 12 is given a more detailed drawing of the frame, A, 
The threads of the screws, c, c, for adjusting the slide wires- 
have a pitch of i mm. In this figure are shown the bobbin, a, 
for carrying the two balancing arms of the bridge, the manganin 
wire being wound noninductively. The metal disk, 6, for support- 
ing the bolometer strips is attached to the bobbin, a, by insulating 

material, t, and is covered with a 
thick (0.3 mm) piece of mica, as 
indicated at o, Fig. 12. 

The details of the bolometer 
strips, 6, 6, and their support are 
shown in Fig. 13. The bolometer 
strips are of platinum o.ooi to 
0.003 ^^ thick, 0.2 to 0.5 mm 
wide, 10 mm long, and have a re- 
sistance of 0.7 to 3 ohms; and are 
soldered to adjustable copper termi- 
nals. Other platinum foil in silver, 
purchased abroad, had a thickness 
of 0.0005 to 0.003 mm (of Pt). 
The heavy copper wires, /, Fig. 9, are soldered directly to these 
terminals, using rosin. 

In Fig. 14 are shown the two hollow fiber sliding contacts. 
The holes for the wires are shown at w, w. It will be noticed that 
these sHding contacts are made hollow by drilling into them, in 
two directions, from the top. In this manner, a mercury holder 
is produced that is open only at the top, "* Since the mercury 
column surrounding the wire, w, w, is 10 to 12 mm long and at 
least 1.5 mm thick around the slide wire, there is no difficulty 
whatever with bad contacts. 

In previous designs at least three different methods were em- 
ployed in connecting the bolometer, galvanometer, slide wire 




Fig. 13. — Support for bolometer strips. 



***The writer is indebted to Mr. Harring, of the instrument division, for his in- 
genuity in fulfilling this condition. 



Coblentz.] 



Instrumenis and Methods o/Radiomelry. 



443 



TOP VIEW 



END VIEW 



and storage battery (see Figs. 15 and 16). The following is a 
modification of the method used by Julius (loc. cit.)- He moved 
the conducting wire leading from the bolohieter to the battery. 
In the present case the wires are stationary and the mercury 
contact piece, d. Fig. 12, mounted on a screw, c, is moved. 
In Fig. 16 is shown the method of wiring the bolometer. The 
heavy copper lead wires are not shown in the figures, except /, 
Fig. 9. The bolometer strips, 6, 6, in Fig. 16 are also to 
be noticed in Fig. 13, while the balancing coils a, a (20 ohms 
each) of manganin are wound 
noninductively on the bobbin, 
a, Fig. 12. The sliding con- 
tacts, d, d, are also shown in 
Fig. 12, where the wires are 
indicated at w, w. The latter 
pass through insulated bush- 
ings in the frame, A, h. For 
testing the sensitiveness two 
fine insulated wires are soldered 
to the ends of the exposed bo- 
lometer strip. Fig. 16. By con- 
necting these wires with a high 
resistance, say 100,000 ohms, 
the deflection obtained by thus 
unbalancing the bridge is a 
measure of the sensitiveness of 
the galvanometer. For pro- 
longed routine observations, a 
shtmt box for reducing the sensitiveness of the galvanometer by 
\f tV> ^» ^> ^^^ rhr» ^ reversing switch and a switch to shunt the 
bolometer, as just indicated, may be mounted in one box, which 
greatly facilitates the work. The largest wires, f\ /", Fig. 16, 
of constantan are 1.4 mm diameter and have a resistance of 0.3 
ohms per meter. By moving the mercury contact 0.0 1 mm the 
change in resistance is 0.000 03 ohm, or by joining the wire as 
shown by the dotted lines. Fig. 16, the change in resistance is 
0.000015 ohm. For the coarse adjustment, constantan wires /', 
/', having a diameter of 0.63 mm and a resistance of 1.4 ohms 




J_ 



5 em 



Fig. 14. — Sliding contact 



444 



Bulletin of the Bureau of Standards. 



\Vol.4.No.3. 



per meter were used. With this combination it was possible to 
balance the bolometer so close (using the coarse adjustment) that 
on permanently closing the galvanometer circuit the deflection 
would be only from 2 to 3 cm, which was then brought back to 
zero by means of the fine adjustment. By connecting the sliding 
contact and balancing coils, as indicated, it is possible to balance 
the bridge with but little adjustment on the ^lide wire, /', f . An 
increase in resistance on one side of the bridge corresponds to a 
decrease on the other side. This permits the use of less wire, 
and the whole can be confined in a smaller space than would have 
been possible in some of the previous instruments if an attempt 
had been made to place the bolometer and balancing coils and 
slide wire in one case. 



S&A 



(€1 




Ii- LANQLEY, SNOW, A8CHKINA88, JUUU8, INQERSOLL, DONATH. 

Fig. 15. — Various bolometer armngements. 

The sliding contact. Fig. 14, containing the mercury is made 
of fiber, which is elastic and makes a close contact, so that no 
mercury works out in sliding it along the wire, w, w. The open- 
ings at the top are closed with cork and there is no danger of 
spilling mercury. It is important to use flexible wire (twisted 
cord) between the bolometer and the galvanometer to reduce 
thermal effects. In the original design it was intended to use 
manganin for the balancing coils and slide wires, because of its 
low temperature coefficient and low thermoelectric power against 
copper. It was foimd that the manganin amalgamated so seri- 
ously with the mercury and became so brittle that constantan 



Codleniz.] 



Instruments and Methods of Radiometry, 



445 



was used for the slide wires in spite of its high thermoelectric 
power, which, however, is of minor importance, since the wires 
are situated in the interior of the case away from the bolometer 
arms, where there are air currents. 

The use of copper for a slide wire (as one writer has suggested) 
is objectionable on account of its high temperature coefficient. 
If the ends of the bolometer arms, where they are soldered to the 
balancing coils, are kept at the same temperature by shielding 
them from radiation, there will be no thermoelectric currents 
developed, and if they are equally warmed the currents developed 
at the ends will be in opposite directions and will neutralize each 
other. The result of the Peltier effect and the Thomson effect 
has never been considered in radiation instruments except in the 
radiomicrometer where Boys (loc. cit.) calls attention to the fact 




OALVANOMETBI 



¥ig. 16.— Arrangement of present bolometer circuit. 

that the exposed junction will not become so warm as it other- 
wise would on account of heat conduction and Peltier action, 
which tends to send a current in the opposite direction to that 
producing it. In a platinum bolometer these two effects as well 
as the thermoelectric power are small " and, since they are opposed 
to each other must have little effect on the quantities measured. 
In iron and nickel the Peltier effect is much larger, and when used 
in a thermopile (Rubens) it is important that the junctions have 
as small heat capacity as possible. 

5. Comparison of Sensitiveness of Various Bolometer-Galva- 
nometer Combinations. — Important data on sensitive radiation 
meters, and particularly that relating to bolometers, are given 
in Table IV. It will be noticed that the thermopile is as sensi- 

^ See Gray, Magnetism and Electricity, and Landolt and Bornstein Tables. 



446 Bulletin of the Bureau of Standards. \voL4yo.3. 

live as the bolometer. By using iron-constantan wire 0.06 
to 0.08 mm thick the high thermal capacity is reduced. The 
resistance will be somewhat higher, but that is not objectionable, 
since the galvanometer resistance may also be made higher. The 
sensitiveness of the radiometer is obtained by comparing it with 
the bolometer. Although the radiometer is less efficient than the 
bolometer, it probably absorbs as much of the incident energ}-. 
Since the radiometer deflections were larger per unit area than 
the bolometer-galvanometer deflections, it is safe to assume that 
the radiometer was just as sensitive as, if not more so, than the 
bolometer. The long period is of course a serious objection in 
certain classes of work. In Table IV it w^ill be noticed that the 
high temperature sensitiveness of the various instruments has 
been attained by the use of a highly sensitive long-period galva- 
nometer, by using a large bolometer current, and by placing the 
scale at a great distance from the galvanometer. Assuming that 
the sensitiveness is proportional to the square of the period for a 
scale at I m, and a bolometer current of 0.04 ampere, it will be 
seen from column 10, Table IV, that the temperature sensitiveness 
of the various instruments falls in two groups. To the first 
group belong the earlier instruments of Rubens, of Snow, and of 
Paschen, with a sensitiveness of about 5° X 10-^ per mm deflection. 
To the second group belongs a more sensitive combination of 
Paschen's, and the writer's instrument, in which i mm deflection 
corresponds to a rise in temperature of ii°Xio-'and g^Xio-', 
respectively. In other words, the instruments of the latter g^oup 
have the same sensitiveness, and any increase is to be attained by 
lengthening the scale distance; the bolometer current of 0.04 
ampere is about the maximum limit for accuracy. The sensi- 
tiveness of the writer's instruments could have been further increased 
by lengthening the scale distance to 2.5 m, when the temperature 
sensitiveness would have been 3?6 X 10-', and by doubling the 
galvanometer period, when the sensitiveness would have been 
9®Xio-^ against Paschen's i°Xio-'. Such a computation is of 
course illusory, on account of damping in the galvanometer. On 
actual trial (but not for the magnet system quoted) for a full 
period of 30 seconds the sensitiveness of the galvanometer was 
i = 7 X 10- " ampere. 



Cob/enir.] Instriimeuis and Methods of Radiotnetry. 447 

6. Comparison of Bolometer with Thermopile. — The eificiency 
of the bolometer and the thermopile is reduced by losses due 
to reflection and radiation from the receiving surface and to 
heat conduction to the unexposed parts. The loss of energy in 
the thermopile due to the Peltier effect has been considered in 
discussing that instrument. The loss of energy due to reflection 
is about 4 per cent (Kurlbatun *^) . Assuming the bolometer 
to be made of platinum 0.5X0.002 mm cross section, and the 
thermopile of 20 junctions of iron and constantan wire 0.06 mm 
diameter, it can be readily shown that the cross section of the 
thermopile is about 56 times that of the bolometer, and from 
their heat conductivities, for the same temperature gradient, that 
the loss of heat by conduction in the thermopile is about 100 
times that of the bolometer. But the temperature gradient at 
the ends of a bolometer strip carrying an electric current may be 
50° to 100°, so that the heat lost by conduction may be about the 
same for both instruments. Since the temperature of the bolom- 
eter is from 50 to 100° higher than the thermopile, the loss of 
heat per second due to radiation in the former is from 2 to 3 times 
that of the latter. But the mass of the thermopile is 5 times, 
while its specific heat is 3.3 times, that of the bolometer. Hence, 
to raise the temperature of thermopile and the bolometer to the 
same extent, 16 (5 X3.3) times as many heat units must be applied 
to the former. Since the loss by radiation is 3 times as great 
from the bolometer, it will require about 5 times as long for the 
thermopile to reach a steady temperature. In practice, however, 
on accotmt of the blackening of the surface, which modifies its 
emissivity, the bolometer is not so quick in its action as here 
computed. 

From these considerations, as well as from the mechanical dif- 
ficulties in constructing a thermopile of wire less than 0.05 mm 
in diameter and keeping the resistance low, it appears that the 
thermopile can not be made so quick in its action as the bolometer, 
and hence is not so well adapted where a quick automatic regis- 
tration of the galvanometer deflections is desired. But, as will 
be shown presently, since it is difficult to read large deflections 

^^'Kurlbaum: Ann. der Phys. (3) 07, p. 846; 1899. Ann. der Pliys. (4) 2, p. 555; 1900. 



448 Bulletin of the Bureau of Standards, \voL4,no.3. 

accurately in less than a 4 to 5 seconds swing of the galvanometer 
system, a thermopile of 0.06 to 0.08 mm wire, which attains a 
steady temperature in this interval of time, is not objectionable, 
and, since it is less disturbed by air currents (being at room tem- 
perature), it may be the more reliable instrument (see Table V). 
Neither instrument, however, compares with the radiometer in 
steadiness. The amoimt of work done on emission, absorption, and 
reflection spectra, as well as the accuracy attained, in the infra- 
red to 1 5/i, where the radiometer deflections were again and again 
only a few tenths of a millimeter, would not have been possible 
with these instruments. In a recent examination of reflection 
spectra of minerals, using a thermopile, the acctu-acy attainable 
without repeating the readings several times was far from that of 
the radiometer, although the actual deflections were larger. 

The present experimental comparison of the thermopile, of 
0.08 mm iron and constantan wire, and the platinum bolometer 
was imdertaken in order to determine the accuracy attainable in 
measiuring a constant source of radiant energy, and hence to 
learn the feasibility of substituting the thermopile for the trouble- 
some bolometer. Within experimental error it has been estab- 
lished by Langley, by Rubens, and by Julius that the bolometer 
(galvanometer) deflections are proportional to the current flowing 
through the bolometer and also to the amount of energy falling 
upon the bolometer strip. It remained, therefore, to determine 
whether the present bolometer behaved likewise and also whether 
the same acctu'acy is attainable with the thermopile. 

To this end a bolometer was constructed with the greatest care. 
It was annealed before adjusting the resistance of the strips, 
covered electrolytically with platinum black after the method of 
Kurlbaum*^ and then smoked over gauze wire over a paraffin 
candle. The resistances of the bolometer strips were 1.782 and 
1.797 (^ = 0.015) ohms, respectively. After blackening them 
they were 1.766 and 1.818 (-^ = 0.052) ohms, respectively. The 
width of the bright strips was 0.50 mm, which was increased to 0.56 
mm after blacking. The length was 11 mm and thickness less 
than 0.002 mm. The bolometer current was 0.04 ampere and 
throughout the following experiments there was no difficulty due 
to air currents. Magnetic disturbances were at a minimum and 



CodlenU.] 



Inslrumenls and Methods of Radiometry, 



449 



conditions for accurate measurements were as perfect as one 
could expect. 

TABLE V. 

Comparison of Bolometer and Thermopile. 



Direct deflection 

(mean value) 



Deflection with 
disk. x8o** 949.9 
(mean value) 



Ratio 



Remarks 



Bolomatar 



(Kay 24, '07) 



12.22 
12.16 



6.14 
6.11 



50.24 
50.24 



Thennopile. 



(May 24, '07) 
13.14 j 



6.61 



14.22 
14.30 



7.21 
7.24 



50.26 



50.7 
50.6 



Nernst heater on 98 volts at 1 m. from 
bolometer. Galvanometer ( fall ) period 
8 seconds uidamped; 50 ohms in series. 
Total deflection about 80 cm. Bolom- 
eter is perfectly steady, and comes 
to rest abruptly. Readings vanr from 
0.1 to 0.7 per cent from mean of about 
10 in each set. Temperature sensi- 
tiveness =6** X 10"*. 



Conditions are the same as for the bo- 
lometer. Thermopile deflections 
" creeps," and does not come to rest 
in the same time as the galvanometer 
( on open circuit or with the bolometer) , 
due to its larger heat capacity. Gal- 
vanometer single swing of 4 seconds is 
increased to 6 seconds and is fully 
damped due to lag of thermopile; 50 
ohms in series with galvanometer. 
Temperature sensitiveness=2°xiO~^. 

Source and disk nearer the screen. Dif- 
ficult to read the deflection on account 
of the " creeping," which amounts to 1 
to 3 mm. Readings made at end of 6 
seconds vary by 0.4 per cent from mean; 
20 ohms in series with the galvanom- 
eter. Temperature sensitiveness^ 
5°xiO-«. 



The thermopile of 0.08 wirt (20 junctions covered with a slit 
0.5 mm wide), already described, showed a slight lag in registering 
the energy received. Although this was not marked, there was a 



450 Bulletin of the Bureau of Standards. [yoi.^.xo.j. 

tendency for the deflection to creep instead of stopping abruptly, 
as in the case of the bolometer. This was most marked in large 
deflections and necessitated exposing the thermopile to radiation 
for a definite time (6 seconds) and taking the zero at the expiration 
of an equal interval of time. The results are given in Table V. 
The last two values for the thermopile are vitiated by radiation 
from the rotating disk, to be explained later. The results show 
that there is no great difference in the two instruments. It was 
necessary, however, to note the time of exposure of the thermopile, 
which is not convenient for large deflections. The estimation of 
the relative merits of the bolometer and the thermopile is, there- 
fore, a personal one, and from the experience gained it may be 
said that for measuring intense sources the bolometer is the more 
accurate (when working to 0.5 per cent) unless great precautions 
be taken in making the thermopile readings. 

The theoretical temperature sensitiveness of the thermopile 
was considerably greater than that of the bolometer, as was found 
on subsequent computation. It may be added, therefore, that if 
the bolometer sensitiveness had been increased by increasing the 
current through it, there would have been greater unsteadiness 
in the galvanometer readings. 

7. Bolometric Usage. — The use of the null method in bolomet- 
ric measurements has been suggested, i. e., to actually measure the 
change in resistance rather than to read the direct deflections. 
Wadsworth^^ has shown, however, that the deflection method is 
quicker and better than the zero method, since it involves no dis- 
turbance of the contacts in any part of the bridge. At the highest 
sensitiveness the zero method is practically excluded for accurate 
measurements of very feeble radiations. 

For the sake of completeness, the method of determining the 
temperature sensitiveness of the bolometer strip is included here. 
The method " consists in unbalancing the bridge by placing a high 
resistance, e. g., 100,000 ohms, in parallel with one of the bolom- 
eter strips and noting the resulting deflection. Then, knowing 
the resistance and the temperature coefiicient of the bolometer 



*' Wadsworth, Astrophys. Jour., 5, p. 268; 1897. 
*- Rubens and Ritter, Wied. Ann., 40, p. 62; 1890. 



cod/eniz.] htstnimeuts and Methods of Radiomeiry. 451 

strip, one can compute the change in temperature, Ji, correspond- 
ing to I mm deflection from the equation : 

^'^. hd 

where r = the resistance of the bolometer strip, ^ = shunt resist- 
ance (100,000 ohms), 8 = the temperature coefiicient (about 
0.003 -+■ for platinum) , and d = the galvanometer deflections in 
mm. Snow" placed a large resistance permanently in parallel 
with the bolometer strip and unbalanced the latter by closing a 
shunt around a part of the former. This method was also 
employed to determine the sensitiveness from day to day. Its 
use is open to one objection, viz, the change in current in the 
bolometer strip introduced by placing a high resistance in parallel 
is sufficient to disturb the temperature equilibrium in the bolom- 
eter case, and it is necessary to wait a few seconds for the galva- 
nometer to become steady. However, since this test is not very 
frequent, it is more convenient than the radiation test. Lummer 
and Pringsheim ** compared the daily variation in sensitiveness by 
exposing the bolometer strip to the radiation from a ** black -body ** 
heated with boiling water. The latter has the disadvantage that 
the amount of atmospheric water vapor as well as the barometric 
pressure varies from day to day, and hence the amount of energy 
received by the bolometer is not perfectly constant. Angstrom,** 
and Kurlbaum *" have given methods for determining the sensi- 
tiveness in absolute value. 

The change in absorption and emission of platinum black and of 
soot with thickness was investigated by Kiurlbaum.*^ He found 
that a deposit of soot weighing 25 mg per dm* emits 94 per cent 
as much energy (at 100° C.) as does a complete radiator, while 

**Snow, Phys. Rev., 1, p. 32; 1893. 

** Lummer and Pringsheim, Wied. Ann., 68, p. 399; 1897. 

** Angstrom, Acta. Reg. Soc. Upsala, June, 1893. 

*• Kurlbaum, Wied. Ann., 51, p. 591, 1894; 61, p. 420, 1897; 65, p. 746, 1898. 

*' Kurlbaum, Wied. Ann. (3), 67, p. 846, 1899. 

The electrolyte used in depositing platinum black consisted of i part of platinum 
chloride, 30 parts of water, and 0.008 of lead acetate. He used a current density of 
0.03 ampere per cm^, and 4 volts for 3 minutes. The lead acetate causes the platinum 
black to adhere. The writer has found that for narrow bolometer strips the platinum 
black deposits more rapidly on the edges than on the flat surface. 



452 Bulletin of the Bureau of Standards. ivoi. 4. so.3. 

a deposit of 83 mg per dm* of platinum black is required to have 
the same emissivity. From this it was assumed the bolometer 
absorbs a similar amotmt. Paschen,** however, appears to be the 
only one who attempted to make his bolometer a more complete 
absorber of radiation by placing it in the focus of a highly-polished 
concave hemispherical mirror, as shown in Fig. 11. He used this 
arrangement in finding the maxima of his energy curves and found 
that the constant, 2920, in the Wien displacement law was in- 
creased about 4 per cent by using the mirror. Another method 
of '* blackening " the bolometer is to have the strip in the form of 
a hollow blackened cylinder with a slit to admit the energy to be 
measured. In this form the resistance of the strip is low, and 
hence there is difficulty in attaining sufficient sensitiveness. 

The adaptability of a radiation meter for a particular kind of 
work seems never to have been considered. The bolometer is 
well adapted for measuring intense sources, using a short period 
galvanometer, but it has not been a great success in measuring 
weak sources of radiation. A very sensitive radiometer behaves 
more like a photographic plate (which is cumulative in its action, 
however) and useful in registering feeble soiu-ces. The thermo- 
pile is the most useful in meastu-ing weak radiation, such as the 
selective reflection of long heat waves (Rubens, loc. cit.) where a 
radiometer can not be used on account of the opacity of its win- 
dow. It is interesting to note that the radiometer has been used 
successfully in measuring heat from stars (Nichols, loc. cit.. Table 
III). It is perhaps the most efficient instrument which can be 
used for such work. This is due to the fact that the star image is 
small. A radiometer with a small vane, the size of the star image, 
will have a short period, and since its sensitiveness may be made 
as high as for a large vane, it is well adapted for such work. On 
the other hand, the number of thermo- junctions that can be 
covered with a star image must be very limited, hence, gain in sen- 
sitiveness must be attained by increasing the period of the gal- 
vanometer. For the same reason the bolometer, on account of its 
large surface, can not be used as efficiently as the radiometer for 
this particular problem. That is to say, the great sensitiveness 

** Paschen, Berichte Berliner Akad., p. 409; 1899. 



CodlenU.] 



Instruments and Methods of Radiometry, 



453 



required would have to be attained through the galvanometer by 
lengthening its period, thus subjecting it to magnetic pertiwba- 
tions. For spectrum energy work, using a fine linear surface, the 
bolometer has been used to great advantage, especially in the 
investigation of the dispersion of fluorite and rock salt. 

(a) Errors Resulting from Lack of Balance of Bolometer. — The 
errors introduced into the observed galvanometer deflections as a 
result of not keeping the bolometer balanced appears never to have 
been considered. It has been frequently noticed in this paper that 
the bolometer is subject to a continuous drift, due to a slow unbal- 
ancing of the bridge arms. In the present test the bolometer was 



em 
20 



19 



o 

p 
o 



18 



17 






-15 -10 -5 +5 +10 

Fig. 17. — Variation insensibUity with balancing of bolometer. 



+15 cm 



unbalanced by moving the mercury contact on the compensating 
wires. The source of energy was a no- volt Nemst-lamp heater 
on a 98-volt storage battery circuit, which supplied a constant 
current. 

In Fig. 1 7 is shown the change in the galvanometer deflections 
(ordinates) when the bolometer is exposed to the radiation from 
the Nemst-heater, after unbalancing the bolometer bridge. The 
amount of unbalancing is given in galvanometer deflections 
(abscissae), positive or negative, depending upon the direction of 
the unbalancing. In Fig. 17 the zero deflection indicates that 
the galvanometer deflection was the same on open and on closed 



454 Bulletin of the Bureau of Standards, \V0L4.S0.3. 

bolometer circuit, i. e., that the bolometer was perfectly balanced. 
The positive and negative deflections indicate the change in the 
zero of the galvanometer reading on closing the bolometer circuit 
after the latter was unbalanced, corresponding to a drift. The 
different series of observations are indicated by dots, circles, 
crosses, etc. The lack of symmetry in the two branches of the 
graph may be due to the galvanometer not being level. The 
galvanometer sensitiveness was about 3 X lo"** ampere, and the 
bolometer current was 0.04 ampere. 

The results show that a lack of balance of 2 cm introduced an 
error of i per cent in the resulting galvanometer deflections. 
From this it will be seen that it is necessary to keep the bolometer 
balanced to less than i cm in order to insure accuracy in the 
final results. 

Vn. SSXECTIVE RADIATION METERS. 

The well-known fact that the resistance of seleniimi changes, 
when exposed to light, has been applied to photometric measure- 
ments. If an alloy could be produced which has its maximum 
sensitiveness (i. e., its resistance change greatest) for those wave 
lengths to which the eye is most sensitive, it would be possible 
to devise a method for measuring radiant efiiciencies which is far 
superior to present methods of comparing the total radiation to 
the luminous radiation. In the ultraviolet the photo-electric 
effect has been applied to measure the radiation from the mercur>' 
arc." 

Little is known in regard to this class of radiation meters. 
Since they are highly selective their application is limited, but 
if the proper combination could be found having a sensibility 
curve similar to the eye it would have a wide application in 
photometric work. If the transformation of radiant energy into 
electrical energy is as complete in the photo-electric effect as in a 
bolometer it would be a steadier instrument, since the former 
is not subject to such perturbations as is the bolometer. 



*®Kuch and Retschinsky, Ann. der Phys. (4) 20, p. 563; 1906, 



codientz.] Insirufnenis and Methods of Radiometry, 455 

Vin. CHANGE m SENSITIVENESS OF INSTRUMENTS. 

Various observers have tested the bolometer and have found 
that as a meter of radiant energy it indicates a direct proportion- 
ality (in galvanometer deflections) , with a change in intensity of 
tjie incident energy. Hence, it is unnecessary to reduce its 
indications by a known amount in order to obtain an accurate 
measure of the energy falling upon the bolometer strip. Large 
deflections of the auxiliary galvanometer, however, are not 
proportional to the current, and hence a shtmt or series resistance 
must be introduced in the galvanometer circuit to reduce the 
deflections to the region within which proportionality holds, or 
the necessary corrections must be applied from the calibration 
curve of the galvanometer. The sensitiveness may also be 
reduced by changing the current in the bolometer circuit. 

On the other hand it has been shown that, on account of the 
Peltier effect, which may introduce errors of about i part in 300 
to 400, it is advisable to keep the equivalent deflections less than 
30 cm (scale at i m) when using an iron-constantan thermopile. 
Since the galvanometer deflections must also be kept small, the 
best procedure is to put a large resistance in series with the 
thermopile. The use of a sectored disk would appear better, for 
then all the errors are transferred back to the disk. However, 
the following experiment shows that the motion of the disk may 
introduce slight errors, which must be determined and eliminated 
in quantitative work. 

(a) Experiment with a Sectored Disk. — In comparing the relative 
merits of the bolometer and the thermopile, the simplest method 
appeared to be to reduce the intensity of the source by a known 
amount, by using a sectored disk the angular openings of which 
are accurately known. It will be noticed that while the ratios of 
energy transmitted by the sectored disk were in close agreement 
in any series of measurements (see Tables V and VI), the numer- 
ical values were in all cases higher than the true ones. In other 
words, the disk transmitted too much energy or the apparent 
opening was larger than the true one. It remained therefore to 
be shown whether this is due to diffraction (of the very long wave- 
lengths) or to lack of proportionality in the registering of the 
energy by the bolometer and by the thermopile. The method 
15298—08 8 



456 



Bulletin of the Bureau of Standards, 

TABLE VI. 
Reliability of Bolometer Measurements. 



\Vol.4.No.3' 



Direct deflection 


Deflection with 
disk 


Ratio 




(mean of 6 to 


xo readinge) 


rt 


Remarks 


DUk opening 240^=66,8% 




(May 27, '07) 








9.42 cm 


6.33 cm 


67.23 


Galyanometer period 8 seconds, and vi- 
bration is undamped; 20 ohms in series 


9.35 


6.28 


67.25 


11.82 


7.95 


67.25 


with the galvanometer. Temperature 


9.11 


6.12 


67.2 


sensitiveness = 6** X lO"*^ C. High 
values are due to radiation from mov- 
ing disk, which is 0.5 m from screen. 


8.94 


6.04 


67.5 


Galvanometer period 14 seconds and 


13.31 


8.99 


67.6 


vibration is just damped. Tempera- 








ture 8ensitiveness=l^.2X10-* C. 



/>»* opening 1W^=SS,406 



(May 28, '07) 

r5.82 
11.56 



(May 27, '07) 
12.31 

30.40 
13.75 



(May 25, '07) 

14.15 
17.04 



5.65 
4.14 



4.28 



10.53 



4.70 



4.75 
5.68 



35.70 
35.75 



34.8 
34.7 

34.5 



33.56 
33.38 



Galvanometer period 14 seconds. 

Galvanometer period 8 seconds. Disk 
better shielded than in previous experi- 
ments and is closer to screen — 6 cm 
from it. Heater 150 cm from bolom- 
eter; screen at 80 cm. 

14 ohms in galvanometer circuit. Gal- 
vanometer period 14 seconds. Nemst 
heater on 74 volts. 

No resistance in galvanometer circuit; 
results show that high value is not due 
to lack of proportionality of galvanom- 
eter deflections. 

Nemst heater on 95 volts. 20 ohms in 
galvanometer circuit. Total deflection 
is about 45 cm. 



Disk opening 180° =50.1^5 



(May 24, '07) 

17.17 cm 
17.21 



8.65 cm 
8.64 



50.37 
50.20 



Nemst heater on 98 volts at 1 m from 
bolometer. Galvanometer period 8 
seconds. 30 ohms in series with gal- 
vanometer. Total deflection about 80 
cm. The individual deflections vary 
from 0.2 to 0.5 per cent from mean. 



CodienuA Instruments and Methods of Radiometry, 457 

of observation consisted in taking from 5 to 10 readings without 
the disk, then a similar number with the rotating disk interposed, 
followed by a number without the disk. 

The first test was to determine whether the rotating disk (30 cm 
diameter, 1.3 meters from the bolometer) affected the instrument, 
and it was foimd that the resulting deflections, i to 2 mm, were no 
larger than those due to stray radiation reflected from the station- 
ary disk. A heav}' black cardboard shield was then placed 
between the bolometer and the disk (0.5 m from the disk) and 
similar screens were placed around the source, which was 2 meters 
from the bolometer. No radiation was detected from the station- 
ary disk, whether the open or closed part of the disk faced the 
bolometer; but unfortunately this test was not made for the 
moving disk. The disk with the 240° opening gave values 0.5 
per cent too high (see Table VI, observations of May 27). The 
results with the 120° disk (6 openings of 20° each) were in still 
greater error. The space between the bolometer and the shield 
was then entirely enclosed, and with the disk close to the opening 
(7 X 10 cm) in the shield the discrepancy became still greater. 
It was then found that the increased transmission is due to the 
moving disk and depended upon the distance of the disk from the 
screen. 

It was further shown that the transmission was proportional 
to the speed, so that the 240° disk (true transmission 66.827 per 
cent^) gave values from 69.3 to 77.2 per cent. In Fig. 18 are 
plotted the galvanometer deflections (abscissae) for different 
distances of the disk from the screen. The latter was 80 cm from 
the bolometer, and had an opening in it which was the size. of the 
openings in the sectored disk. No radiation was observed from 
the stationary disk, nor from the shields back of it when the open 
sector was before the bolometer. The speed of the disk was such 
as is used in photometry, and was kept constant for each series of 
observations. In the lower curve for the 240° disk the speed 
was slow and there was a flicker on viewing it. The curves show 
that the maximum radiation occurs when the disk is about 6 cm 
from the shield, and it disappears immediately on stopping the 
disk. 

* These disks and their constants were supplied by Dr. Hyde. This Bulletin, 2, 
p. I, 1906. 



458 



Bulletin of the Bureau of Standards. 



irol. 4, jVo. J, 



The disk was run continuously for a complete series of measure- 
ments, and no deflections greater than i to 2 mm were observed 
from it immediately after stopping the rotation. In these tests 
the motor was shielded from t>»e bolometer. On removing the 
shield and the disk and on running the motor the deflections were 
from I to 3 mm. The experiment shows that the sectored disk 
is not as applicable as one would suppose, unless one determines 
the corrections which in two series of experiments were found to 
be in very close agreement. In the present curves the galva- 
nometer was at its full sensitiveness (no resistance in series) , so 



cm 
3 



I- 
z 



I- 
o 

Id 2 

























































^ 


JT^ 


~*^ 


--. 


















X 




, V 


~*^ 


' ■ 




h^ 


"O.^ 


:s*.^ 


240" DH 


"< Uf 


EED 1 


& 2 






















































1 


^ 




S 


^ 




















^^ 


^ 




^^ 











120*" 


DISK 



















2 4 6 8 10 12 

DISTANCE OF DISK FROM SCREEN 



14 



16 



18 



20 



22 



24 cm 



Rg. 18. — Radiation from moving sectored disk. 

that in the actual experiments (Table VI) the error was less. 
For the 240^ disk where the error in the deflections was only i 
or 2 mm the correction reduces the observed values close to the 
true one. 

In connection with a bolometer or a thermopile it is possible to 
run the disk at a very much slower speed than used here; this will 
reduce the errors in question to a minimum. 

From the consistency of the ratios in each series, which is of the 
order of 0.2 to 0.3 per cent, it will be noticed that the bolometer 
is a very reliable instrument in spite of its mechanical weakness. 



codunijt.] Instruments and Methods of Radiontetry. 459 

XI. SUMMARY. 

The present paper deals with four instruments for measuring 
radiant energy, viz, the radiomicrometer, the Unear thermopile, 
the radiometer, and the bolometer with its auxiliary galvanometer. 

As a result of this historical inquiry and by experiment it was 
shown that the radiomicrometer is capable of great improvement, 
by reducing its weight, by lengthening its period, and by placing 
it in a vacuum. It was further shown, that on account of para- and 
dia-magnetism the sensitiveness of the radiomicrometer is very 
limited, perhaps only a fifth of the best bolometers described. 

It was also shown that the Rubens thermopile is as sensitive as 
the best bolometer, and that its heat capacity can be greatly 
reduced by using thinner (0.06 to 0.08 mm diameter) wires, which 
are made shorter, thus keeping the resistance low. The computed 
errors, due to the Peltier effect, are about i part in 300. The 
thermopile is not so well adapted as is the bolometer for instan- 
taneous registration of radiant energy and it does not admit so 
great a range in variation of sensibility, but on account pf its 
greater steadiness it commends itself for measuring very weak 
sources of radiation, e. g., the extreme ultra-violet and infra-red 
region of the spectrum. 

By a direct comparison it was shown that the radiometer can 
be made just as sensitive as the bolometer, but its period will be 
much longer. It was found that the radiometer is not selective 
in its action, and hence that it can be used for measuring ultra- 
violet radiation. The main objection to the use of a radiometer 
is its long period, but since it is easily shielded from temperature 
changes, and since it is not subject to magnetic perturbations, 
this long period is of minor importance so long as we are dealing 
with a constant source of radiation. In spectrum energy work 
its usefulness is limited to the region in which the window is 
transparent, to 20/A. The fact that the radiometer deflections 
can not be obtained in absolute measure is a minor objection, 
since in but few cases (thus far at least) has it been necessary to 
thus obtain the deflections. The action of a radiometer is some- 
what analogous to a photographic plate, in that it will detect weak 
radiation, provided one can wait for it, and, on account of its great 



460 Bulletin of the Bureau of Standards. \yoi.4.No.3. 

steadiness, is of all the instruments considered, probably the best 
adapted to search for infra-red fluorescen/te. 

A bolometer installation is so distributed that it is diflScult to 
shield from temperatm-e changes. In spite of its small heat 
capacity, the bolometer has a ** drift 'y due to a slow and unequal 
warming of the strips. Air current^ which result from the hot 
bolometer strips also cause a variation in the deflections of the 
auxiliary galvanometer. Nevertheless, despite these defects, it is 
the quickest acting of the four ins^ments considered and is the 
best adapted for registering the ^ergy radiated from a rapidly 
changing source. For precision work it is necessary to keep the 
bolometer balanced to less thauf i cm deflection. 

The auxiliary galvanometer fe the main source of weakness in 
measming radiant energy, and in places subject to great magnetic 
perturbations a period greater than 5 seconds, single swing, is to 
be avoided. Hence, although a greater sensitiveness is possible, 
the working sensibility of the various galvanometers studied is 
of the order of i = 2Xio"*° ampere per mm deflection on a scale 
at I m. Under these conditions the various bolometers used 
were (as a fair estimate of the recorded data) sensitive to a tem- 
perature difference of 4X10"*^ degree to 5X10"* degree per mm 
deflection, on a scale of i meter. The galvanometer sensibility 
was found to be closely proportional to the period. 

A direct comparison was also made of the relative accuracy of 
the thermopile and the bolometer in measuring intense and 
weak sources of radiation, and the results show that there is little 
preference, other than a personal one, in these two instruments. 

The manner of reducing the sensitiveness of these instruments 
is of importance in precision work. The use of a rotating sectored 
disk for reducing the intensity of the source is liable to introduce 
errors, which must be taken into account. 

It may be added that these tests were made in a building which 
is isolated from mechanical and magnetic disturbances, and 
hence imder the most favorable conditions. 

Washington, October i, 1907. 



A QUARTZ COMPENSATING POLARISCOPE WITH ADJUST- 
ABLE SENSIBILITY. 



By Frederick Bates. 



All of the polarizing systems so far devised for quartz wedge 
polariscopes have been defective for one of two reasons; either 
the sensibility of the instniment can not be varied or it can be 
used only with monochromatic light. The system which has 
given the best results and is in general use at the present time is 
the so-called half -shade. It introduces into polarimetry the 
photometric principle, inasmuch as the angular position of the 
analyzing nicol is determined by bringing the two halves of the 
field of the instrument to a condition of uniform illumination. 
In any half -shade system the light from the polarizer is plane 
polarized in two planes which make an angle a, called the polari- 
zation angle, with each other. All of the light illuminating 
either half of the field is thus polarized in one of these planes, and 
when a setting is made the polarization plane of the analyzer 
makes approximately a right angle with the bisector of a. Upon 
the magnitude of a depends the accuracy with which settings 
can be made; the sensibility for any given light source being an 
inverse function of that magnitude. Hence it is exceedingly 
desirable that a polarizing system permit a to be varied as the 
observer may desire. 

A monochromatic light-source of sufficient intensity and suita- 
ble for the average work for which quartz compensating polari- 
scopes are used is yet to be obtained. In order to obviate this diffi- 
culty the rotation produced by the substance being examined is 
compensated as completely as possible by the use of oppositely 
rotating quartz. Since the polarization planes of the different 

461 



462 Bulletin of the Bureau of Standards. {Voi.4.1^0.3. 

wave-lengths are thus returned to their original positions, white 
light can be used. This, however, makes it necessar>' for the polar- 
izing system and the analyzer to be mounted so as to be immov- 
able. The polarization plane of the analyzer then makes approxi- 
mately a right angle with the bisector of a. 

The systems most used in polariscopes are the Laurent, the 
Jellet, and the Lippich. In the former a thin plate of quartz cut 
parallel to the optic axis covers one-half the field of the polar- 
izing nicol. In order that the two rays of the doubly refracting 
quartz may combine to give plane polarized light in the analyzer 

they must have an optical difference of path equal to -• Thus 

the thickness of the quartz must be such as to make it a half -wave 
plate and its use is then limited to a light source giving only that 
particular wave-length. The advantage of this system is due to 
its adjustable sensibility, a being twice the angle between the 
optic axis of the plate and the plane perpendicular to the princi- 
pal section of the polarizer, can be readily varied by rotating the 
polarizer. The Jellet system consists of a twin nicol so made 
that the principal sections form the angle a. Since the different 
sections are cemented together the sensibility can not be varied. 
It can, however, be used with white light. In the Lippich system 
a is formed by two beams of plain polarized light which come 
from two separate nicols, one of which covers but one-half the 
aperture of the larger nicol. By rotating either of these nicols 
a can be varied as in the Laurent polarizing system. 

In designing quartz compensating polariscopes the best results 
so far have been obtained by using a Lippich polarizing system 
and a white light-source. The greatest weakness has been the 
lack of an adjustable sensibility. Only one value of a can be 
used and it must necessarily be large enough to give suflScient 
light to read for example the darkest colored raw sugar solutions. 
When polarizing substances having a small coeflScient of light 
absorption, as the better grade of sugars, and the observer has 
more light than he needs he still has available only the sensibility 
which corresponds to that value of a which gives suflScient light 
to polarize substances with a relatively large coeflScient of ab- 
sorption, such as very dark raw sugars. If then it were pos- 



( 



\v 



OF 



Bull. Bur. of Standards. 



Vol. 4, No. 3. 




Fig. 3. — Quartz Compensating Polariscope. 



BaUs.] 



Quartz Compensating Polariscope, 



463 



sible to retain the white-light source and at the same time have 
a adjustable, a distinct advance in polariscope construction 
would be made. 

Let OB and 0B\ figure i, be the traces of the polarization 
planes of the large and small nicols of a half-shade polarizing 
system. If the intensities of the light in OB and OB' are equal, 
the polarization plane EE' of the analyzing nicol will be at right 
angles with OH, the bisection of a. If a be increased or dimin- 
ished by displacing OB' about the point O it is evident that when 
a match is again obtained EE' will have suflfered one-half 
the angular displacement 

through which OB' has been n b 

rotated. However, in the 
Lippich system, since the 
smaller nicol covers one-half 
the field of the larger, we do 
not have the two beams OB 
and OB' of equal intensity. 
If the intensity of OB is A , 
the intensity of OB' is A 
cos*a 




Rg. 1. 



When EE' is set for 
a match the angle between 
EE' and OH is therefore never 90° for any value of a except O, 
The condition for equal illumination with a half-shade system is 

A, sin' ^i~A,sin» d^^O (i) 

where Ai and A, are the intensities of their respective halves of 
the field and 0^, and 0^ are the angles HOB and HOB'. 
Let 

Equation (i) becomes 

A, sin* (<^zbS) = A, sin" (<^=fS) 
From (2) we obtain 

tan t— =fc -'y— - — tan ^ 
y/v + i 



464 Bulletin of the Bureau of Standards. \voi. 4,1^0.3, 

or since 

where J^ — '-r and S is the angular difference, for any value of a, 

between the positions of EE' for a match when i4, = i4i and when 
A^ — Ay cos*a. It is thus evident if a be varied by rotating OB' 
about the point O, that to obtain a match EE' must be rotated in 
the same direction as OB' and by an amount such that the normal 
to EE' always makes an angle 3 with OH the bisector of BOB', 

It would seem a diflScult task to build a mechanism that would 
maintain EE' in the proper position to satisfy the theoretical 
value of h given by (3). If such a mechanism were obtained 
the observer could detect no difference in the intensities of the two 
halves of the field, once the instrument was adjusted, no matter 
what value a might be given. The limits of accuracy in ordinary 
polarimetry are such as to make such a mechanism unnecessary. 
If EE' should always be maintained at right angles to OH, the 
fixed zero point of the instrument would be in error by the amount 
S for any value of a, provided the instrument had been pre- 
viously adjusted for a=0. If the zero of the instrument be 
adjusted to read correctly for any particular value of a and then 
a be changed, the zero will be in error by the difference between 
the values of S corresponding to the two values of a. The curve 
in figure 2 shows the value of S, obtained by solving (3), corre- 
sponding to any value of a between 0° and 15°, From this 
curve it is at once evident that with an instrument equipped 
with a Lippich polarizing system, in adjustment for a polarization 
angle a =10°, a may be varied between the limits of 4® and 
i2?4 without introducing an error due to a change in the zero 
point greater than o?i S (sugar degrees), provided EE' be con- 
stantly maintained at right angles to OH. If the zero point be 
adjusted for a=8?5, a may be varied from 0° to ii?5 with a 
maximum error of o?i S; or from 5?6 to io?3 with a maximum 
error of o?o5 S. 



Bates,] 



Quarts Compensating Polariscope. 



465 



The instrument shown in figure 3 was built ^ for the Bureau 
of Standards to fulfill the theoretical conditions mentioned above. 
It is a double quartz wedge compensation instrument with a 
Lippich polarizing system. The analyzing nicol and the large 
nicol of the polarizing system are moimted in bearings and are 
joined by gears with a connecting rod. The milled head of this 
rod is shown half way between the base of the instrument and the 
observing telescope. When the milled head is rotated the two 
nicols are rotated, and the design of the gears is such that the 
analyzing nicol always receives one-half the angular displacement 





s 




























/ 


a3 


ul 




























f 





























/ 






Ul 


























V 

































9 






(C 


























/ 
































f 






3 
























/ 








CO 
























/ 








z 
























/ 






0.2 


























/ 








•0 






















( 


r — 































/ 
































/ 
































/ 










N 






















/ 










Z 




















y 












Ul 




















/ 

































f 










0.1 


Z 


















> 


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< 


















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z 


















y^ 

























^^ 




^ 


a IN 


)EGRE 


E8 











10 11 



12 



IS 



14 16 



01 234 5678 

rig. 2. 
of the large nicol of the polarizing system. Around the milled 
head is a circular scale which shows the polarizing angle for any 
position of the nicols. The milled heads on the right and left 
hand sides of the instrument drive the quartz wedges of the com- 
pensator, and their position is such as to permit the arm of the 
observer to rest free from strain while making a setting. The 
wedges can instantly be clamped rigid for any part of the scale. 
The scales on the quartz wedges are the type used on regular 
Fric saccharimeters. Being of glass and read by transmitted 
light, the scale divisions are exceedingly clear and there is no 



* The builders were Messrs. Josef and Jan Fri6. Prag, Krai. Vinohrady, 233, Austria. 



466 Bulletin of the Bureau of Standards, [ voi. /. so.3. 

black dividing line between a scale and its vernier. In all re- 
search work where small temperature corrections are to be made 
it is necessary to know accurately the temperature of the quartz 
wedges. Polariscope builders seem to have ignored this fact. 
A thermometer ( 10^-40° C, in one-fifth degrees) , with a horizontal 
scale and with its bulb between the quartz wedges, has accord- 
ingly been mounted in a brass case on top of the metal box con- 
taining the compensator. 

For all ordinary sugar testing, where the temperature of the 
room changes slowly, the reading of this thermometer is practically 
the temperature of the room. The observer is thus able to take 
the temperature with the same facility that he reads the scale 
on his wedge, since the thermometer scale is in a similar position 
and is illuminated by the same light source. The base of the 
instrument has been made exceptionally heavy and is mounted 
on rubber tips to insure against accidental change of position 
relative to the light source. 

The improvements are equally advantageous for all uses to 
which the polariscope may be put. However, it is in the testing 
of sugars the new instrument should find its broadest application. 
With the instrument in adjustment for a polarization angle of 
10° the observer can instantaneously adjust the sensibility so as 
to have sufficient light to polarize the darkest sugars, or he can 
with equal facility have an instrument far more sensitive than 
any ordinary saccharimeter. In measuring rotations with the 
greatest possible accuracy, or when it is desired to make the 
settings with the least possible strain on the eye, the observer has 
only to change the polarization angle until he has just sufficient 
light to bring the two halves of the field to the same intensity. 
He then has for his eye an instrument so adjusted as to give the 
maximum sensibility for making the setting, no matter what the 
character of the substance whose rotation is being measured. 
With the instrument adjusted for a — the observer soon learns 
the exact change in the zero point of the scale for all values of a, 
and instantly makes the sUght correction mentally for each value 
of a used. He is thus able to determine the polarization of the 
better grades of sugar to an accuracy of =t.oi° S. 

Washington, October 15, 1907. 

O 



AN APPARATUS FOR DETERMINING THE FORM OF A 
WAVE OF MAGNETIC FLUX. 



By M. G. Uoyd and J. V. S. Fisher. 



The apparatus here described was designed and constructed in the 
course of measurements upon the magnetic losses of energy in sheet 
iron. Its object was the determination of the average vahie of an 
alternating electromotive force from which the form factor of the 
emf. wave and the maximum value of the magnetic flux inducing 
it can be computed. It serves equally well, however, for the tracing 
of a wave of magnetic induction, and that use of the apparatus is 
described in the present article with illustrative examples. 

DESCRIPTION OF APPAfiATUS. 

The essential part of the apparatus is a rotating commutator 
which reverses the contacts twice per cycle. An ebonite disk is 
mounted on a shaft between bearings ; to its circumference is fas- 
tened a thin conducting strip with gaps at two points i8o° apart. 
Four brushes, equally spaced, bear upon the metal rim of the rotat- 
ing disk, and their joint action is that of commutation. A carrier, 
of brass, having four arms, is mounted loose upon the shaft ; the 
arms support the brush holders. Screwed fast to the carrier is 
a gear wheel which meshes with a worm. A graduated circular 
scale is attached to the carrier, and is read by means of a fixed index 
fastened to the base. 

By means of the worm and gear the brushes may be set in any 
desired position. The brushes are thoroughly insulated from each 
other and from the carrier by means of ebonite strips at the extremi- 
ties of the arms. 

467 



468 Bulletin of the Bureau of Standards. \voi. 4, ao. 4. 

The shaft of the rotating commutator may be coupled directly to 
the generator shaft. The instalment was designed for use with a 
four-pole machine, running at 1800 revolutions per minute. 

Fig. I shows a photograph of the commutator in position for use. 
The principal dimensions are: 

Circumference of disk 56 cm 

Thickness of metal rim i. 5 mm 

Width of gaps in rim 2 mm 

Gear diameter, 96 teeth 10. 2 cm 

The wheel gearing with the worm on the end of the shaft makes 
an electrical contact for every hundred revolutions of the shaft. 
This serves to record the speed of rotation. 

Referring to Fig. i, the brushes a c are connected to a secondary 
coil wound around the flux to be measured. The brushes * d are 
connected to an indicating direct-current instrument, such as a 
d'Arsonval galvanometer or Weston voltmeter. Any instrument 
whose deflection is proportional to the first power of the current will 
answer the purpose. 

To plot a curve of magnetic induction, a reading on the Weston 
instrument is taken for a definite position of the brushes. Then 
successive readings are taken, the brushes being advanced the same 
number of degrees each time until they have been shifted 180? 
In practice it sufiices to shift the brushes only 90°, corresponding 
to a half cycle, since the readings repeat themselves in the second 
quadrant when only the odd harmonics of the fundamental frequency 
are present, and the apparatus is suited only to waves of this char- 
acter. This condition means that the positive and negative lobes of 
the wave shall be similar, a condition which will be fulfilled if the 
magnetization is produced by a well-designed and well-constructed 
generator. 

THEORY OF THE METHOD. 

Let ^ = magnetic flux to be determined. 
T — its period. 

e — instantaneous emf. induced in secondary coil. 
N —• turns in secondary coil. 
/ = time of commutation. 

F= reading of voltmeter, to which commutated emf. is 
applied. 



Bull. Bur. of Standards. 



Vol. 4. No. 4. 




Fig. 1. — Rotating Commutator with Adjustable Brushes for Tracing Magnetic Waves. 



-MV5«5lTf 



?N 






^^^^ ] Wave Form of Magnetic Flux. 469 

Then 

e = — TV— ■ 

(P= — jjr \edt is the change in flux during the time 

expressed by the limits of integration. In the present case the 
integration is carried on between two reversals or a half period and 
is repeated during the following half period in the reverse direc- 
tion. 



Hence ^t^T-^t= — J^ 



n T 

1^+2 

J/* 



Now, if positive and negative lobes of the wave are similar, 



'"^J, ' 



T 

^t+^= — ^t Also,^ I e dtvs the reading of 



1/ T VT 

the voltmeter V. Or - 2 CP. = — ^^ and 0* = ^—t-. 

Nz AtN 

This shows that the value of the magnetic flux at any instant is 
proportional to the algebraic average of the induced emf. during 
the succeeding half period. Since the emf. must change sign when 
the flux passes through a maximum, this maximum will be given 
by the average value of the emf. during a half period beginning 
with its zero value. If the wave of magnetic flux has only one 
maximum during a period, as is usually the case, then the emf. will 
remain positive during the half period next succeeding the maxi- 
mum, and the average value of the emf. will be a numerical aver- 
age. In this case the reading of the voltmeter will give what is 
commonly known as the ''average value of the emf." If to the 
secondary coil another instrument be directly connected whose indi- 
cations are proportional to the square of the emf., as a dynamome- 
ter or electrometer, this instrument will give the " effective value " 
of the emf. and the ratio of the two readings will give the form 
factor. ^ 

If, however, the flux wave be so much distorted as to include a 
dimple between two maxima, the emf. will change sign during the 
half period, the algebraic average will no longer be a numerical 



470 



Bulletin of the Bureau of Standards, 



\Vol.4.No.4. 



average, and the form factor as determined above will not agree 
with the customary definition of form factor. 

The apparatus can also be used to plot curves of electromotive 
force or current. For this purpose the emf., or current, is applied 
to the primary of an air transformer, the secondary of the same 
being connected through the rotating commutator to the Weston 
voltmeter, and readings taken as before. 




Fig. 1.— Waves of Magnetic Flux, June 5, 1907, 
Period = 0.0333 sx. 



Bfnaas=^0,000 gausses. 



The principal source of error in the apparatus is in the imperfect 
contact of the brushes, and the breaking of the contact upon revers- 
ing. The contact resistance is a variable and uncertain quantity. 
It is desirable, therefore, to have a circuit of high resistance, so 
that the maximum value of the contact resistance is a negligible 
part of the whole. This was accomplished in the experiments cited 
by using a very sensitive Weston instrument, giving full scale de- 
flection with about 0.0004 ampere. Resistance sufiiciently high to 
make the inductance error negligible, could be connected in series. 

This difficulty can be avoided by using an electrometer as indi- 
cating instrument. In this case the two pairs of quadrants are 
connected to the commutator brushes, while the needle is kept 
charged to a constant high potential. 



Uoyd. n 
Fisker.\ 



Wave Form of Magnetic Flux. 



471 





^:=:- 



i\ 




■X 



-^ 



r 



V 



\ 



f\ 



\ I 
I 
I 

I 



.• ^_ 



■\- 



Fig. 3. — Waves of Electromotive Force Corresponding to the Flux Waves of Fig. 2. 



472 Bulletin of the Bureau of Standards. \yoi,4,No.4, 

If the terminals of the indicating instrument are reversed when 
the emf. is passing through zero there is no appreciable loss due to 
reversal; but if the reversal occurs at any other time, the reading 
will be not quite equal to the integrated value of the emf., since 
certain elements in the integration are lost during the time the 
circuit is broken during reversal. If the brush be made wide 
enough to bridge the gap on the commutator, so that one contact 
is made before the other is broken, the instrument is short-circuited 
during the overlap, and again the reading is too low. In the instru- 
ment described the breaks occupy 1.4 per cent of the time of a c>'cle, 
supposing the brushes to make a line contact. As the brushes are 
applied tangentially, with pressure, they spring into the air space 
and make the interval of break much less than this. Its exact 
value will depend upon the speed and has not been determined. 
For points near the maximum of the flux curve the elements lost 
are insignificant, and for points near the zero, where they become 
important, a larger percentage error may be tolerated. 

Error may also arise from unequal spacing of the brushes, but it 
is not difficult to make this error negligible. 

EXAMPLES OF USE. 

Several examples of flux waves determined with this apparatus 
are shown in Fig. 2. The corresponding emf. waves induced in 
the surrounding coil, as determined with the oscillograph, are given 
in Fig. 3. 

The wave form was altered by taking the magnetizing current 
from two generators in series, the frequencies being 60 and 180, 
respectively. The two generators have their shafts coupled together 
so that the speed and phase relation remains constant during any 
run. By varying the excitation of the two generators a wide varia- 
tion in wave form is obtained; by reversing one of them, a dimpled 
emf. wave is changed to a peaked one, etc. Fig. 4 gives some addi- 
tional examples of waves of magnetic flux. 

In order to test the degree of accuracy obtainable, an iron ring, 
made up of a number of thin sheets, was used, and the wave form 
of the flux in the ring plotted out in the manner already described. 
The coil wound on the ring was then connected through a non-induc- 
tive resistance to the primary of a mutual inductance whose secondary 
in turn was connected to the rotating commutator, and a second set 



Uoyd. -| 
Fisher.j 



Wave Form of Magnetic Flux. 



473 

of readings taken in order to secure the wave form of emf. The 
readings are given in Table I, the commutator advancing six degrees 



/ /'V 




/ / / 


\\ 



i 



Tig.A.—WavesofMifgneticFIux. Nov, 11, 1907, Ring No. 31, B^nax= ^0,000 gausses. 

Period — 0.0333 sec. 

each time; the curves plotted from these 15 equi-spaced ordinates 
are shown in Fig. 5. 

Next each of the waves was analyzed into its component sine 
waves by a method given by Lyle,* and the proportions of the har- 
monics present, as well as the phase relations, were thus determined. 
The constants of the circuits were as follows : 
Mutual inductance, 0.0552 henry. 
Resistance of primary of same, 212 ohms. 
Resistance of secondary with voltmeter, 3560 ohms. 
Resistance of voltmeter circuit when connected directly to 

coil, 33560 ohms. 
Turns in coil, 315. 
Maximum flux, 23500 maxwells. 
Frequency, 30. 

*T. R. Lyle, Phil. Mag., 11, p. 25; 1906. 



474 



Bulletin of the Bureau of Standards. 



\Vol.4,No.4. 



TABLE I. 



Flux 


Electromotive Force 


Degrees 


Voltmeter Readings 


Degrees 


Voltmeter Readings 


52 
46 
40 
34 
28 
22 
16 
10 
4 

- 2 

- 8 
-14 
-20 
-26 
-32 


-351 
- 17 
+306 
550 
689 
738 
742 
726 
721 
753 
812 
873 
903 
843 
650 


-38 
-32 
-26 
-20 
-14 

- 8 

- 2 
4 4 

10 
16 
22 
28 
34 
40 
46 


—712 
-571 
-300 

- 33 
+ 104 
+143 
+118 
+ 39 

- 19 

- 16 
+ 51 
+ 181 
+397 
+603 
+719 



The equation found for the flux wave is 

<P=944 sin a+-223 sin 3 (a- 7^24')+ 14 sin 5 (a- 14*^3') 
+ 3 sin 7 (a+- 19^40') 
and for the emf . 

^=430 sin (a— 90° 20') +295 sin 3 (a— 38^41') 
+ 30 sin 5 (a-34°6')+4-6 sin 7 (a+9°45') 

where a is measured from the point where the fundamental of the 
flux wave crosses the axis, and the amplitudes are in divisions of 
the voltmeter and involve the constants of the circuits. To find 
whether the two waves are consistent, we make the amplitudes of 
the two fundamentals alike and then integrate the emf. wave. 

^=1000 sin a+236 sin 3 (a— 7^24')+ 15 sin 5 (a— 14^3') 
-|-3sin7(a+i9°4o') 



IJoxd. -| 
Fi5her.\ 



Wave For7n of Magnetic Flux. 



475 



^=iocxD sin (a— 90° 20') +686 sin 3 (a— 38°4i') 
+ 70 sin 5 (a-34°60+ii sin 7 (a+9°45') 
— r^da=icxx) cos (a— 90° 20') + 229 cos 3 (a— 38^41') 
+ 14 cos 5 (a-34°6')+2 cos 7 (a+9°45') 

= 1000 sin (a— o°2o')+229 sin 3 (a— 8^41') 
+ 14 sin 5 (a— 16°6') + 2 sin 7 (a+22°36') 



1000- 




750- 



tooo- 



Fig. 5. 



The accuracy of determination of the phase angle decreases as 
the amplitude decreases, so that it may be in error several degrees 
with the higher harmonics. This is especially true where only 
fifteen ordinates are used. The discrepancy in phase for the funda- 
mental is only 20', and if the fundamentals were brought into 
agreement, it would be less than one degree for the third harmonic. 
The principal discrepancy to be noted is in the amplitude of the 
third harmonic, amounting to seven units, or 0.7 per cent of the 
amplitude of the fundamental. An accuracy of better than one per 
cent is not to be expected from the present apparatus, as the brushes 
can be set only to the nearest 0.1°, and on a steep part of the 
cur\^e this may cause an error in the reading of an ordinate, which 
would amount to one per cent of the maximum amplitude. In an 



476 Bulletin of the Bureau of Standards, [^oi, /. .vo. 4. 

apparatus intended primarily for the accurate plotting of waves, 
means should be provided for a more accurate setting of the 
brushes. 

Forty-five ordinates are read when greater accuracy is sought. 
The third, fifth, ninth, and fifteenth harmonics are then easily 
separated, and the seventh and any higher ones desired are after- 
ward found in the usual way. 

COMPARISON WITH PSEYIOUS METHODS. 

The first recorded waves of magnetic flux were computed by 
mechanical integration of the curve of secondary emf. 

Sahulka" in 1898 described an apparatus similar to the present 
and based upon the same principle. He utilized, however, only one- 
half of the cycle, and his circuit was open seven-eighths of the time, 
and hence he did not obtain such steady readings on the voltmeter. 
This becomes of importance at low frequencies. Townsend' con- 
structed a similar apparatus, utilizing half of each wave. 

Lyle* has also utilized the same principle in a wave tracer, which 
may be used to determine the harmonics separately, as well as the 
total wave. He uses carbon brushes, and while no dimensions are 
given, the illustrations would indicate that the errors due to losing 
certain elements in the integration might be large. This source of 
error is not considered by him. 

To Blondel * has been ascribed the idea of using an oscillograph 
whose galvanometer needle should have no control and no damping. 
The second differential of its angular position with respect to time 
would then be proportional to the instantaneous current. A coil 
surrounding the flux to be measured is connected to the primary of 
a transformer with air core, the secondary being connected to the 
galvanometer. In this way a current is secured which is propor- 
tional to the second differential of the flux with respect to time. 

We have been unable to find any published description of such 
an apparatus or of its performance. 

Washington, November 15, 1907. 

» J. Sahulka. Zs. f. Elektrotechnik, 16, p. 4; 1898. 

■F. Townsend. American Inst. Electrical Engineers, Trans. 17, p. 5; 1900. 

*T. R. Lyle. Phil. Mag., 6, p. 549; ^1903. 

* Electrician, 49, p. 172; 1902. 



EFFECT OF WAVE FORM UPON THE IRON LOSSES IN 

TRANSFORMERS. 



By Morton G. Lloyd. 



It has long been known that the iron loss in a static transformer 
is dependent upon the form of the wave of electrical pressure which 
is applied to its primary winding, since the form of this wave, with 
the constants of the transformer, determines the wave of magnetic 
flux produced in the iron core. In 1895 Dr. Roessler* read a paper 
before the Verband Deutscher Electrotechniker in which he pre- 
sented the results of experiments, using two generators whose curves 
of electromotive force were quite different. With the same emf. 
applied to the transformer, the iron losses were decidedly less with 
a peaked emf. wave, corresponding to a flat wave of magnetic flux. 
He also pointed out that when the form of wave is not a sine curve, 
it is necessary to modify the formula of Steinmetz for iron losses 
by introducing the form factor of the emf. wave. 

As the Bureau of Standards possesses facilities for supplying emf. 
waves of any desired form, the present investigation was undertaken, 
at the suggestion of Dr. E. B. Rosa, for the purpose of shedding 
additional light upon this question. The problem is first considered 
from the theoretical standpoint, and the results of experiments are 
given in which various wave forms were used with commercial types 
of transformers. The wave fonns were obtained by using a series of 
generators* giving approximately sine waves of frequencies 60, 180, 
300, 420, 540, 660, 780, and 900 cycles per second when running at 
normal speed. The phase relations of the several generators are 
adjustable, and as they are mounted upon a single shaft, remain 

'G. Roessler. Electrician, 86, p. 124; 1895. 

'A fuU description of this set of generators wiU be given in a subsequent issue of 
this Bulletin. 

477 



478 Bulletin of the Bureau of Standards. [yot. 4, -yo. 4- 

invariable during an experiment. By connecting these generators 
in series and exciting each to the proper voltage, any desired wave 
form which involves only the odd harmonics up to the fifteenth may 
be procured. 

1. THEORETICAL. 

Let IV = power expended in the cor^ pf a transformer. 
W^H = power expended in hysteresis. 
IVe = power expended in eddy currents. 
B = maximum flux density in the iron, the flux being 

assumed uniform. 
17 and f be constants depending upon the iron. 
^ = ratio of hysteresis to total iron loss. 

n = — = frequency of applied emf. 

f r= form factor of induced emf. 

e = instantaneous value of induced emf. 

JS = effective value of induced emf. 

E = average value of induced emf. for a half period. 

A = amplitude of fundamental component of induced emf. 

A = ratio of amplitude of harmonic to amplitude of funda- 
mental. 

m = order of harmonic. 

= phase angle of harmonic. 

/ = time since fundamental passed through value zero in 
positive direction. 

ti = time at which e=o. 
__ 2irt 

" r 

The subscript zero applies to the case of a sine wave. 

Definitions. 






1. The effective value of a periodically varying quantity is the 
square root of the average value of the square of that quantity. 

2. The form factor of a periodically varying quantity is the ratio 

of its effective value to the algebraic average value during the half 

T 
period from t^ to t^ + - . 



iJaytL] Effect of IVavB Form upon Transformers, 479 

We assume the iron losses in the transformer to be represented by 
the modified form of the Steinmetz formula, 

= rinB''^-\-i;f^n^S' 

The induced voltage in the primary winding of a transformer differs 
from the applied voltage by the amount of the ohmic drop, or dif- 
ference of potential due to resistance. As the ohmic drop is small, 
and as consideration of it introduces difficulties, we shall consider 
only the induced voltage. Commercial voltmeters measure the 
effective value of the voltage. We assume consequently that with 
different wave forms the effective value of the induced voltage is 
the quantity kept constant. This approximates closely to practical 
conditions. 

Since the induced voltage depends upon the rate of change of the 
magnetic flux, its average value at a definite frequency is propor- 
tional to By and its effective value to fB. If the effective value be 
kept constant, the term in the above formula representing eddy cur- 
rents will be constant at any definite frequency. The only change 
in W^ will arise from an alteration in B^ which must accompany any 
alteration inf. 






={(-^-i5')"-] 

If B—B, be small in comparison with B„ this may be written 

, B-B, 

''^^-BT 

If B and q be known, the change in power may be calculated. 

q may be determined approximately by runs at two frequencies, 
using sine waves and voltages proportional to the frequencies. One 
frequency n^ and voltage should be those used with the varying 
22832—08 — 2 



480 Bulletin of the Bureau of Standards, [V01.4.N0.4. 

wave forms. Under these conditions the total flux remains constant 
and B is constant. Hence 

and by subtraction, after dividing by frequency, 



from which 

n. w« 

It remains to determine B for various forms of the emf. wave. B 
is proportional to the average value of the induced voltage during 
the time in which the flux changes from a positive maximum to a 
negative maximum. We assume the positive and negative halves 
of the wave to be alike. This is true of the emf. wave of any well- 
designed and well-constructed generator, which will therefore contain 
only the odd harmonics of its fundamental. 

Any such emf. may be represented by the equation 

e=A sm -j^+AA^ sm \ j^ + ^9) 

+Ah, sin(^-^+^.)+^A, sin (^^+^,) 



+ 






JT 



V2 



uoyd.^ Effect of Wave Form upon Transformers, 481 

In our case E is to remain constant. For the sine wave -£*= -p 
Hence 



A, ^i^h,'+h:+ . . . 






f sin </wr<^+^ I ^A5sin(3<^+^,)rf<^ 
=^[^cos <^,+^A, COS (3^+<?,)+iA,cos(5<^.+<?,)+ • • • •] 

TT 

If the harmonics are in phase with the fundamental 
o=^5=tfj=^T = etc. and ^1 = 0. 

E=^(.+t+t+ . . . . ) 

B, E, ^.V ■^S'^S'*' ) Vi+A,*+V+V+. • • 



The form factor has the value 






and for a sine wave 






482 Bulletin of the Bureau of Standards. \voi.4.no.4' 

If any of the harmonics are reversed in phase, tf = 180°, and the 
corresponding term in the expression for E is negative. This case 
can be included in the case where ^=0 by considering negative 
values for A. 

One Harmonic. 

Let us consider the case where a single harmonic is present. 

E = 5f^Ccos ^, + - COS {m^,->r6\ 
TT \ tn I 

If the harmonic be in phase with the fundamental 

2Ai 



E = 



'h% 



k_ 

B_ E J^ ^ 

If h be negative, or the harmonic reversed, the loss will always be 
less than with a sine wave. This corresponds to a peaked wave for 
w = 3, w = 7, m = ii^ etc. 

If A be positive, the loss may be greater or less according as 

1-1 — is greater or less than ^i-f A«, and the loss will be imchanged 
tn 

when these two expressions are equal. For small values of A, 

h. 

I -|- — is greater, and the loss is increased. With increasing values 
m 

of h the loss reaches a maximum, decreases again to the value for a 

sine wave, and then goes lower. 

The value of h which leaves the loss unchanged is found by 

equating the numerator and denominator of the expression for ^- 



m 
from which 



'+^=Vi+A' 



2m 



uoyd.] Effect of Wave Form upon Transformers, 483 

For maximum loss the derivative with respect to h will ,be zero. 






d>i 



which gives 



~m^i-\-ie V "^W 



+A') 



1^=0 



A=- 



m 



For large values of w, the maximum occurs for a value of A which 
is one-half the value for no change, and in any case at approxi- 
mately one-half. 

The values of h which give a maximum loss and which give the 
same loss as a sine wave, are to be found in the adjoining Table I. 

TABLE I. 



m 


k 


(1,)'-' 




For Maximum Lou 


For Unchanged Loss 




0.333 


0.750 


1.088 




.200 


.417 


1.032 




.143 


.292 


1.016 




.111 


.225 


1.010 


11 


.091 


.183 


1.007 


13 


.077 


.155 


1.005 


15 


.067 


.134 


1.0035 



The maximum value of the loss depends upon(— J , which may 

be obtained by substituting the value of h for the maximum and 
expanding. 

(r=(^)"=(^)"=(v^r=(-^r 



_ ,0^ 0.08 0.032 
"~ w""" w* ' m^ 

These values also are given in Table I. 



484 



Bulletin of the Bureau of Standards, ivoi. 4. -vo. /. 



In Fig. I the values of IpT'^— i are plotted for various values of 

h and for the harmonics from ^^ = 3 to »? = I5. Two sets of curves 
are drawn, one for tf =0 and one for tf = 180°. An ordinate of one of 
these curves multiplied by q is the change in iron loss for the given 
case in terms of the loss for sine wave. 




—0.10 
-0.125 
—0.15 
-0.175 
—0.20 
-0.225 
—0.25 



SSS 





35 



40 



5 10 IS 20 25 30 

PERCENTAGE OF HARMONIC 

Tig. 1. 

If we give h the same value in the case of different harmonics, the 

loss depends upon nt. For tf =0, -^ is larger, as m is smaller. But 

B R 

fortf=i8o°,o is less, as ;« is smaller. The two values of ^ lie 

nearer together the higher the order of the harmonic. The cur\'es 
of Fig. I illustrate this very clearly. 
If A be proportional to m or h = km 

B _ i + k 



uoyd.] Effect of Wave Form upon Transformers. 485 

and the loss is less the greater is m. For small values of k the 
decrease is nearly proportional to n^. 

If h do not exceed the value for no change in iron loss when 
tf=o, there will be some value of 6 which will leave the loss 
unchanged; for in changing Q from 0° to 180° the difference in 
loss changes from an increase to a decrease. 

In this case E = Eo ^^^ hence 

t 

Vi+A' = cos <^j+- COS {m <l>^+0) 

By definition e=o when ^=^1 or 

sin <t>i+A sin {m <f>i + 0)=zo 

These two equations are sufficient to determine <^ and ft The 
form of the equations makes it easier to solve for cos ^1 or cos 
{m (t>i+0) rather than for sin <^i. Since <t>^ is a small angle, greater 
accuracy is attained by solving for cos (m tl>i+ff). 

Let 

m <f>i + 0=v 



Then 



cos' 



Also 



fjL=cos 9iH — cos V 
m 



sin (f>i=—A sin v 
I— cos* if>i = A* sin* 2/=A'(i — cos* v) 

Eliminating cos <f>i and solving for cos v we get 



cos 



''=*(^5[-''+^^'<"""-">+"] 



Substituting numerical values will give v; <f>i is then obtained from 

sin <^, = — A sin v 
and finally from m <f>i-\-0=v. 



486 Bulletin of the Bureau of Standards. ivoi. 4, m. 4. 

If the proportion of harmonic varies inversely as its order, v is 
roughly constant. 
For let mh^k 
Then 



cos 



As m increases, the value of the bracket increases and the value of 
the coefficient decreases, both in small degree ; the largest change is 
in the coefficient, and may amount to about 10 per cent. 

We see on inspection also that if h be small, is about 90°. 
Fo^ Q^v—m <f>i and (f>i is of opposite sign to z/, cos v in this case 
being a small quantity and v consequently a large angle. The 
larger is m^ the smaller must A be to give the same value of 0. 

To illustrate by a numerical example let /« = 3, A = 0.20 
Then ^ 

cos z/=-^(— i.oi98dbi.2962)=o.5i825 or —4.34 

^;==b58<>47^5 <^ = q=9"5i' 

tf=db88°2o' 
Again, let »« = 5, A=o.'i2 

cos 2'=^[- 1.0072=1=1.3057] =0.5188 

^==t58<^45' <^, = =F5°5y-3 

tf==t88°ii'.5 

For the case of ;«= 3 and various values of A, the values of have 
been worked out as shown in Table II and plotted in Fig. 2. This 
curve shows how decreases from 90® to 0° as A increases from 
zero to the limiting value given in Table I. If A exceed this value, 
the loss will be decreased for every value of 0. The curve resembles 
closely an ellipse, but is somewhat fuller than either an ellipse or a ^ 
cycloid with the samesemiaxes. The curve has no simple equation, 
as may be seen by reference to the expressions used in calculating 
its coordinates. 

Other curves have been plotted in Fig. 2, each connecting points 
representing the same loss, the value of the loss being different for 



uoyd.\ Effect of Wave Form upon Transformers. 487 

each locus. Each line represents a change of two per cent in the 

(F V'® 
~- 1 ; the lines inside the "no-change" curve representing 

increased loss, those outside decreased loss. 

TABLE II. 
Calculation of phase angle for unchanged loss with third harmonic. 



h 


1*- 


cos V 


V 


sin V 


siD^l 


*1 


9 


0.0 


1.0000 


0.0000 


900 0' 


1.0000 


0.0000 


(JO 0' 


900 0' 


0.1 


1.0050 


0.2876 


730 17' 


0.9577 


0.0958 


50 30' 


89047' 


0.2 


1.0196 


0.5182 


58° 48' 


0.8553 


0.1711 


90 51' 


88O20' 


0.3 


1.0440 


0.6832 


46° 54' 


0.7302 


0.2191 


12039' 


840 51' 


0.4 


1.0770 


0.7985 


370 1' 


0.6020 


0.2406 


13056' 


780 49' 


0.5 


1.1180 


0.8800 


28° 22' 


0.4750 


0.2375 


13044' 


69034' 


0.55 


1.1413 


0.9117 


24° 16' 


0.4108 


0.2260 


130 4' 


630 27' 


0.6 


1.1662 


0.9388 


200 9' 


0.3445 


0.2067 


11056' 


55057' 


0.65 


1.1927 


0.9622 


15048' 


0.2723 


0.1770 


100 12' 


460 24' 


0.7 


1.2207 


0.9824 


10^46' 


0.1869 


0.1306 


7031' 


33019' 


0.75 


1.2500 


1.0000 


00 0' 


0.0000 


0.0000 


00 0' 


00 0' 



So long as the emf . passes through the zero value only twice per 
cycle, there is little difficulty in determining the value of <f>^. It is 
only necessary to find where ^=0. If, however, the emf. cross the 
axis more than this number of times, it becomes necessary to discrimi- 
nate between the different values of <f> for which e=o. This takes 
place only in cases where there are secondary maxima in the flux 
curve, and it is of course the highest maximum which must be 
located. For any half wave of emf. the number of crossings will be 
an odd number, and they are alternately in the same direction as 
the fundamental wave and in the opposite direction. Those in the 
opposite direction represent minima, and this class includes the 
case ^=0 for tf = 180° with a large component of harmonic. In the 
previous work we have taken ^j = for ^= 180°, but this holds only 
when there is but one value of <f> for which ^=0 in that half wave. 
The limiting values of h to avoid secondary maxima in the wave of 
magnetic flux are given in Table III for ^=0 and tf=i8o°. For 
other values of ^, the limiting values of h may be taken from the 
curves of Fig. 3. 




OF "^h-t 



UNIVERSITY 
















• 
• 


















/ 


/ 

/ 
/ 
f 








1 












/ 

/ 
/ 

/ 


















1 
/ 


/ 








/ 










/ 








// 


7, 










/ 






A 


/. 


// 














A 




y 


y 


/ 




f 






// 


A 


/ 


/ 


/ 






1.1 

1 
1 
1 


6: 


/ 


/> 


/ 


X 


-^ 








1 
1 
1 

1 
1 
I 


/ 


// 


y 


V 


/^ 










t 

1 
1 

' / 


-^z 


// 


/ y 


A 


r 




^^^\ 




/ 
/ 

1 

1 

1 


// 


y 


V 


'/ 


/ 

/ 






\ 


\ 


t 

1 
1 

\ 

1 1 


' k 


►» / 


// 


/ / 
/ 
/ 

/ 
/ 


/ 

/ 


/^ 




\ 

\ 
\ 
\ 
\ 
\ 


\ 
\ 
\ 


If 

If 
1/ 


1 


r L 


/ 1 


I? / 


/ 


f 


\ 


\ 

\ 




/ 


// 


1 i 


/ k 


/ 
/ 


/ 
/ 
/ 
/ 




\ 


\ 
\ \ 
\ \ 
\ 
\ 
\ 




\ 


// 




D / 


/ 
/ 

/ / 

/ f 


2^ 


/ 


\ 


\ 
\ 
\ 

1 




1 5 
1 1 


i 


' 


1^ 


/ 
/ 


' / 


/ 


.^» 








1 1 
1 1 

1 1 
1 i 




1 








/ 
/ 
/ 

/ 










1 1 
1 1 
1 1 

1 1 
i t 



Su, I 



488 



OINOWUVH 



itorrf] Effect of Wave Form upon Transformers. 

TABLE III. 



489 







Limiting Values of h 




vt 










tf-o<' 


»-x8oo 


3 


1.000 






0.333 


5 


.800 






.200 


7 


.613 






.143 


9 


.490 






.111 


U 


.407 






.091 


13 


.347 






.077 


15 


.302 






.067 



It will be noticed that the limiting values of h for tf = 180° are the 
same values which give a maximum loss when ^=0; viz, A =— ' 

lOOr 



m 



90 

80 
O 

O70 

2 



U 











-— 


■-- 








































"''■'-^ 


4 


'^ 






















--. 




















'^ 




















"^ 


~^ 
















\ 


V. 












^ 












^ 




^ 








-^ 


\ 










— 










"^ 


?7- 








\ 


^ 






\ 


S. ' 






::::: 




— , 


_^ 




"^ 


9 








-^ 










\ 




"■ 




— 


i:^ 




5s 


F 








■-^ 


->^ 






'V 


N 


















? - 








= 


=:= 








^ 



































10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180*> 
PHASE ANGLE 9 

Fig. 3. —Umiting Values of Harmonic. 

The value of ^^ is to be chosen from those values of ^ for which 
the emf. curve crosses the axis in the same direction as the funda- 
mental, and that value of <f> should be taken which will give the 
largest average emf. If the curve of the emf. has been plotted, it 
can often be seen from inspection which is the desired value. Thus 
in Fig. 4 the average should be taken between a and rf, which 
gives two larger lobes positive and the smallest lobe negative, since 
it is obvious that this will be larger than the average between c and 



490 



Bulletin of the Bureau of Standards. 



\Vol.4^^^o.4. 



f which includes a negative lobe of medium size. The average 
between b and e is yet smaller and represents a minimum in the 
curve of magnetic flux. 




In the case of a large component of high harmonic the value of 
^1 can be determined approximately from inspection. The har- 

monic will pass through zero every time <f> changes by — , and one 

of these zero values will be at =^. This will be verj*^ close to 

the value of ^ for which ^=o and for which 4>=4>iy but will be 
slightly further from <^=o. This results because the fundamental 
,has relatively small values in this neighborhood and the harmonic 
is changing very rapidly. 
We may say then 



= — cos— + — cos(— w — \-0) 
IT ^ M. tn tn J 

2AV 6 .h'X 
= — cos- +- 

TT L W ^ J 



The extreme values of £ occur for ^=o and ^=i8o°, and this 
approximation includes the extreme values of the true E- <^ is 
always zero for tf=o, and in that case 



:=^0+i) 



Lktyd.] Effect of Wave Form up07i Transformers, 491 

as in the original derivation. The range of variation is from i to 

6 
cos—, and this is smaller, the larger is m. 
m 

If we let w/=i5, ^=180° 

E = ^^cos 12° + — 1=-— 10.978+— I 
TT V m/ •"■ \ mf 

or the range of variation in E is about 2.2 per cent. 
If w=i3 tf=i8o° 

E= -^cos 13 51 +-)= — (o.97iH — I 
TT \ mf ir\ ^' mf 

a range of nearly three per cent. 

We see, then, that with a large percentage of high harmonic the 
loss is always decreased, and the amount of decrease varies only 
slightly with the phase angle. 

There is another effect which must be considered when the emf. 
passes through zero more than once per half cycle, that is, when the 
wave of magnetic flux has more than one maximum. We have 
assumed that the hysteresis is proportion^ to the i.6th power of the 
maximum flux density. The assumption is at least approximately 
true when the iron is put through a simple cycle, but no validity is 
claimed for it in cases where the magnetic flux does not progress 
continuously from a positive maximum to a negative maximum. 
If there be more than one maximum to the half cycle, there will be 
an extra or secondary loop in the hysteresis curve, and greats 
power will be consumed. The formula worked out does not strictly 
apply to such cases. A quantitative examination of actual cases 
shows, however, that this extra power will seldom amount to as 
much as one per cent of the whole, and consequently may usually 
be neglected. Only when one of the harmonics enters to the same 
order of magnitude as the fundamental does this source of error 
become important. Thus with fifty per cent of the fifth harmonic 
the extra loop is through a range of only four per cent of B^ and 
this would not add more than one per cent to the hysteresis loss. 

Figure i is based upon values of E taken for ^1 = 0, and conse- 

(B\^ 
^- 1, except within the limits 



49^ Bulletin of the Bureau of Standards. \voi.4,No.4. 

given by Table III. These limits are shown on the figure by the 
dotted lines. For values of h only slightly in excess of the limit- 
ing values, however, the effect upon E and the extra loops of 
hysteresis are both negligible, and the curves may be used somewhat 
outside of these limits. 

For higher values of h the actual loss would be greater than that 
calculated by use of the curves, and the discrepancies will be greatest 
for tf =180°. 

Numerical Example with one Harmonic. 

When q has been determined for a given frequency, the change 
in iron loss may be determined for ^=0° or ^=180° by reference 
to the curves of Fig. i. For other values of 6 the value of ^^ must 
be determined before B can be calculated. This can be done by a 
graphical method, or by successive trial and calculation. 

Thus let »« = 3, A =0.20, y = o.6o 
For tf=o, or a flat voltage wave, 









=1.075 
0.045 



an increase of 4.5 per cent 
For tf = 180°, or peaked voltage wave 

^^:=i^= -0.080 

a decrease of 8.0 per cent 
The results for intermediate values of 6 are given in Table IV. 



uoyd.'\ Effect of Wave Form upon Transformers. 

TABLE IV. 



493 



• 


*i 


-'1 


(i^)- 


W-W. 

in Per Cent 


0° 


0° 


1.067 


1.075 


-h 4.5 


± 30 


=F 3.7 


1.061 


1.065 


-h 3.9 


d= 60 


=F 7.15 


1.044 


1.038 


+ 2.3 


± 90 


=F 10.0 


1.018 


0.997 


- 0.2 


rh 120 


qp 11.5 


0.985 


0.946 


- 3.2 


db 150 


=F 10.0 


0.951 


0.895 


- 6.3 


±L 180 


0. 


0.933 


0.867 


— 8.0 



Two Harmonics. 
In this case 



: = ^[cos <^,+^|cosK<^,+^0+^;cosK ^,+<?.)] 



^0 v^+v+v 

If the harmonics be not in phase with the fundamental, any special 
numerical case can be worked out by finding the value of ^j corre- 
sponding to definite values of 0^ and tf,. 

If the harmonics be assumed in phase with the fundamental, <^i = o 
and 



i+i' + *' 



m. 



m. 



If welet Ai = A, 



A ^1 + 2 h' 



and there will be some value of h which will leave the loss unchanged. 
Let w«i = 3, w,= 5, then 

from which A =0.622. 



494 Bulletin of the Bureau of Standards. [voL4,no.4. 

Again, if the fifth harmonic be reversed in phase 

and h = O.I 346. 

Again, we may assign a definite value to h^ and find the value of 
A, which leaves the loss unchanged. Let Ai = o.2, ^1 = 3, m^=^, 

from which A =0.611 or —0.167, 

indicating that the fifth harmonic may be introduced in reversed 
phase with magnitude one-sixth of the fundamental, or in same 
phase with magnitude 61 per cent of the fundamental. 

Several Harmonics. 

Going back to the general expression for E, we have 

^ ^rcos<^,+|«cos(3<^,+^3)+|»cos(5<^,+^,)+ 1 

^' ■yli+h.'+hJ+h^T^. 

The numerator of this expression may be either greater or less 
than unity, depending upon the values of ^3, ^5, etc. The de- 
nominator is independent of the phase relations and is never less 
than unity. We may consider the influence of the two factors 
separately. The denominator always tends to decrease the loss; 
for small values of h by an amount proportional to A* and for larger 
values by an ever decreasing proportion. Superposed upon this 
decrease is the effect of the numerator. When the numerator is 
greater than unity, it may overpower the denominator for small 
values of A, but can not do so for the larger values. If a number 
of harmonics are introduced at random, the probability is that the 
loss will be decreased, and the greater the number of harmonics, 
the greater the probable decrease. For with various phase angles 
some of the terms in the numerator will counteract others, while 
in the denominator all work together for a decrease. 

In special cases the higher harmonics may be present in greater 
magnitude than the lower ones, but more often their amplitude is 



B^ 
A 



ijoyd.^ Effect of Wave Form upon Transformers. 495 

small, and we will consider the case where h is inversely pro- 
portional to the order of the harmonic. 

Let k=ih^=5h^ = jh^^ etc., <^i=:o, ^=0 or 180°. 
Then 

'•""V-4+?+7- • ■ • •) 

If >t<i, an accuracy of one per cent will be attained by disregard- 
ing harmonics above the ninth. If each 6 be zero, 

^<-k^i>- ■■■) 

If in this case we let k=o.^, q=o.6 

B W- W^ 

-^^=1.074 —^--=0.071 

It is readily seen that the lower harmonics and especially the 
third will be predominant, unless it be introduced with 6 near 90°, 
and even then its influence in the denominator is unimpaired. 

It is to be noticed that the expression for ^ also represents the 

ratio -^ ; in other words, an increase or decrease in loss depends upon 

whether the form factor of the wave of voltage is less or greater 
than the form factor of a sine wave. In the special cases previously 
considered, where the loss is unchanged, the form factor has the 

same value as for a sine wave, namely, — p= 1.1107. 

We may express the percentage change in loss as 

— ^F— *=d \ f\ — I or 1.6 y ^~r' whenyi— / is small compared 

to yC It is not necessary, therefore, to know the components of the 
wave used in order to calculate the loss. // is sufficient to deter- 
mine the form factor. This can always be done if apparatus is 
22832—08 3 



496 Bulletin of the Bureau of Standards, \voi.4.no.4. 

available for tracing the wave', and the more laborious process of 
analyzing the wave may be omitted. 

If we define a " peaked " wave to be one whose fonn factor is 
greater than 1.1107 and a " flat" wave to be one whose form factor 
is less than 1.1107, then we may make the general statement that 
a peaked emf . wave reduces the iron loss of a transformer and a flat 
wave increases the iron loss. If we have a third harmonic combined 
with the fundamental, the peaked wave occurs when 6=. 180° or with 
the maxima of the two components coinciding in time. With the 
fifth harmonic we again have a peaked wave for tf = 180°, but in this 
case the positive maximum of the fundamental is coincident with 
the negative maximum of the harmonic, and from mere inspection 




rig. 5. 

the curve would hardly be classed as peaked. These two cases are 
illustrated in Fig. 5. It is not desirable, consequently, to define a 
" peaked " wave as one having coincident maxima for fundamental 
and harmonic, for then "peaked" and "flat" would cease to be 
discriminating terms. Defining the wave by means of the form 
factor, its nature is determined largely by the value of tf, and if a 
single harmonic be present, the wave will always be peaked when 
90°<^<i8o° and will usually be flat when 6 is near zero. This 
can usually be judged upon inspection by the steepness of the curve 
where it passes through zero. 

2. DESCRIPTION OF APPARATUS. 

The power expended in iron losses was measured by means of 
a dynamometer wattmeter.* The fixed coils are in series connec- 
tion with the primary winding of the transformer; the movable 
coils are connected, with a suitable multiplier, to the terminals of the 

'The form factor can also be determined directly if apparatus is available for meas- 
uring the averafi^e value of the emf. Such an apparatus is described b j Lloyd and 
Fisher, this Bulletin, p. 501, and by Rose and Ktihns, E. T. Z., 24, p. 992; 1903. 

*This instrument is of the type described in this Bulletin, 1, p. 424, by Rosa, Lloyd, 
and Reid. 



uoyd.^ Effect of Wave Form upon Transformers, 497 

secondary winding. If the secondary contain the same number of 
turns as the primary, and enclose the same magnetic flux, the watt- 
meter then measures the energy supplied to the core and to the sec- 
ondary circuit or circuits. If the turns be not the same in number, 
their ratio gives the factor connecting the wattmeter reading with 
the true watts. As only relative values are desired in the present 
investigation, it is unnecessary to know this factor. This method 
has an advantage over the more usual method of applying the 
primary voltage to the potential circuit of the wattmeter, since the 
copper loss in the primary is not included in the measurement. 
Usually this must be determined and applied as a correction. 

To get the iron losses alone, a correction must be applied for the 
energy supplied to the secondary circuits. The energy expended in 
a noninductive secondary is equal to the square of the effective 
voltage induced in that secondary divided by the resistance of the 
secondary circuit. In the present work this correction is small and 
constant, and may be neglected in considering relative losses. 

The induced voltage was measured by a dynamometer voltmeter 
which in most cases was connected to a secondary winding. This 
instrument measures the effective voltage and its deflection was 
kept constant during a series of runs. Its inductance was known, 
and the effect of high frequency currents was compensated by slight 
changes in its noninductive multiplier. In some of the runs this 
voltmeter was connected across the primary terminals, notably 
when the secondary voltage was low and the component of high 
harmonic large, as in these cases the voltmeter correction would 
otherwise become very large. This method of connection keeps the 
applied effective voltage constant and thus more nearly fulfils the 
conditions of commercial operation. It does not keep the induced 
voltage so constant, however, and thus does not so nearly realize the 
conditions assumed in the theoretical deductions. In the cases 
where both methods of connection were used in turn, the difference 
in the results was less than one per cent. 

A Thomson ammeter of the magnetic vane type was inserted in 
the primary circuit and readings of the magnetizing current were 
made. No use of these readings is made in the present work. 
The resistance of this ammeter is 0.4 ohm, of the field circuit of 
wattmeter 1.7 ohm, a total of 2.1 ohms in series with the primary. 



498 



Bulletin of the Bureau of Standards, 



\Vol.4,No.4. 



No rheostat was used in this circuit, the applied voltage being con- 
trolled through the field excitation of the generators. As the pri- 
mary current in most cases was about one ampere, the ohmic drop 
in the instruments was only about two volts. 

The connections are shown in the diagram, Fig. 6. 

When the transformer used had two secondaries, the voltmeter and 
potential circuit of wattmeter were connected to separate windings. 
When there was a single secondary, the two were connected in par- 
allel to its terminals. The deflections of the wattmeter were taken 
as proportional to the watts, when the multiplier R remains con- 
stant This is true for deflections not differing more than a few 




Fig. 6. — Diagram of Connections. 

centimeters, as is the case in these measurements. In determining 
^, the multiplier R was changed to give the same wattmeter deflec- 
tion on both frequencies, and the watts taken to be proportional to 
the resistance of the potential circuit. Calibration of the instru- 
ment was therefore unnecessary. 

The frequency of the generator was measured by a Hartmann- 
Kempf frequency meter of the new type, containing an indicator for 
each half cycle. By reference to this instrument the frequency 
could be read with greater accuracy than J^ cycle, which was con- 
sidered sufficient. Sixty cycles was the frequency used in the 
measurements, and the proper speed of the generator was main- 
tained by adjustment of the field resistance of the driving motor. 



uoyd.] Effect of Wave Form upon Transformers. 499 

As this motor was supplied with current from a storage battery, the 
changes in speed were gradual, and the necessary adjustments slight 
and infrequent. 

The transformers used were : 

1. General Electric Co., Type H, No. 290645, 120/4 volts, 60 
cycles, 2,000 watts, ^=0.61. 

2. Siemens and Halske No. 6700, 120/2 volts, 50 cycles, 1,600 
watts, ^=0.60. 

3. General Electric Co., Type H, No. 290414, 480-240-120/30- 
60-120 volts, 60 cycles, 500 watts, ^=0.70. 

Transformer No. i was operated at no volts, and No. 2 at 132 
volts, 60 cycles being used throughout. Otherwise the conditions 
were normal, and the transformers were operated under no load. 
In this case the ratio of transformation is not influenced by the 
wave-form.* 

No. 3. has four separate primary windings and four separate 
secondaries, which can be connected in series or parallel, thus per- 
mitting various ratios of transformation. 

3. OBSERVATIOKS. 

When starting a series of observations, the primary voltage was 
adjusted to the desired value on sine wave by reference to a calibrated 
portable voltmeter. The reading of the volt-dynamometer was taken 
at the same time, and the same deflection was maintained through- 
out the series by adjustment of rheostat in generator field. Read- 
ings were then taken on the wattmeter with sine wave, and followed 
by readings with other wave forms. At frequent intervals through- 
out the series the sine wave was again used, and control thus kept 
of the changes due to heating. If current be kept on, the iron loss 
continually decreases on account of the heating, and a reading on 
any wave form must be compared with the mean of sine wave read- 
ings before and after. Every result given is the mean of three 
observations taken in immediate succession, the voltmeter being set 
independently for each. At the beginning or end of the series 
observations were taken at 30 cycles, in order to determine the pro- 
portion of hysteresis to the total iron loss. For this purpose the 
multiplier of the voltmeter was changed so as to make the total 

*G. Roessler, Electrician, 86, p. 151 ; 1895. 



5CX) Bulletin of the Bureau of Standards, \voi,4.no.4. 

resistance of its circuit just one-half of the previous value, and 
adjustment made for the same deflection. The voltage must then 
also be one-half of the previous value. 

In using distorted waves which involve higher frequencies the 
voltmeter must be corrected for its inductance error. The correc- 
tion is easily made for a sine wave, and most conveniently by alter- 
ing the resistance so that the impedance remains constant Let L 
be the inductance of the instrument. Then, if the multiplier be 
noninductive and R be the total resistance, the impedance is 



V^T^^'Z*=^(i+^^7 



To have the impedance the same as with direct current, the resist- 

ance must be changed to R^ = R — {L is ver>' small com- 

R 

pared to Ry its value being 0.138 henry.) With a distorted wave 
the resistance required by the different components is different, but 
by giving proper weight to each component (i. e., in proportion to 
the square of the amplitude) we get 

Hence, in changing from the sine wave to a distorted wave, we 
change the resistance of the multiplier by 

2z!^(A>.'+v<+ ) 

To determine the components of the wave used, the magnetizing 
circuit is broken after adjustments have been made, and the voltage 
of each generator is measured with a Stanley hot wire voltmeter. 
This is done on no load to avoid the drop on the line. As the load 
is very small compared to the capacity of the generators, the arma- 
ture reaction does not appreciably affect the voltage. 

The procedure in taking observations is illustrated by a run taken 
to determine the dependence of the result upon the way of connect- 
ing the voltmeter. The readings are given in Table V. 

Each of the deflections given for voltmeter and wattmeter is the 
mean of three observations. The calculated effects are submitted 



Lloyd.] Effect of Wave Form upon Transformers. 

TABLE V. 
Effect of Voltmeter Connection. 



501 



Transformer No. a. q»o.6o, m— 3 








Voltmeter 


Wattmeter 


h 


Resistance 


Deflection 




Deflection 


Increase 

due to 

Harmonic 


Increase 

in 
Per Cent 


0. 




25000 


27.95 


Prlmaiy (132 VOlti) 








0. 




25000 


27.95 


Prlniaiy 


20.16 






0.23 


180° 


25000 


27.95 


(( 


18.25 


-1.80 


-9.0 


0.23 


00 


25000 


27.95 


<( 


21.01 


+0.88 


+4.4 


0. 




25000 


27.95 


f f 


20.12 






0. 




500 


19.35 


{(132 Volts on Prlmaiy) 








0. 




500 


19.35 


Seoonduy 


19.77 






0.23 


180° 


499 


19.35 


<( 


17.84 


-1.91 


-9.7 


0.23 


0° 


499 


19.35 


II 


20.61 


+0.89 


+4.5 


0. 




500 


19.35 


ti 


19.70 






0.23 


180° 






CalcoUted 






-9.3 


0.23 


0° 












+4., 



for comparison. They are readily obtained from Fig. i. A similar 
set with transformer No. i, using 21 per cent of fifth harmonic, gave 
—0.8 per cent and —3.0 per cent, with voltmeter on primary; 
—0.9 per cent and —3.4 per cent, with voltmeter on secondary. 

The agreement with each other and with the calculated values 
are seen to be well within one per cent, and this is about the order of 
discrepancies throughout the work. 

The value of q for the above transformer was determined from 
the observations given in Table VI, with the voltmeter connected 
to secondary. 

The observations were jnade with the help of Mr. J. V. S. Fisher, 

to whom credit is also due for assistance in the computations and 

drawings. 

4. EXPERIMENTAL RESULTS. 

Table VII gives the results on two transformers of introducing a 
single harmonic either in phase or reversed. For comparison the 
calculated effects taken from Fig. i are added to the Table, those 
marked with an asterisk lying outside the limits set by the theoret- 
ical conditions. 



502 



Bulletin of the Bureau of Standards. 
TABLE VI. 



\yol,4.ffo.4' 



Tmnsformer No. a. Sepsmtion of Hysteresis and Eddy Current Losses 





Voltmeter 


Wattmeter 


n 


Hyster- 
esis 


Eddy 
Currents 






Res. 


Defl. 


Res. 


Defl. 


Q 


60 
30 


500 
250 


19.31 
19.31 


900 
359 


20.05 
20.04 


15.00 
11.97 


8.94 
8.94 


6.06 
3.03 


.596 
.747 



Table VIII gives the results of shifting the phase of the har- 
monic, while keeping its magnitude constant, and these are plotted 
in the curves of Fig. 7. The calculated values in Table IV may 
be compared with the corresponding column, of Table VIII, viz, for 
transformer No. 2, ni = ^. 

TABLE VII. 





m 


h 


Percentage Increase in Loss 


Transformer 


«« 


0° 


«»z8o° 




Exp. 


Calc. 


Ejtp. 


Calc 


No. 1 


3 


.11 


42.8 


+3.0 


-4.0 


-4.1 


a tt 


5 


.105 


+1.7 


+1.5 


—2.8 


—2.6 


ti a 


7 


.19 


+0.7 


+0.9 


-3.8 


-4.3* 


t€ tt 


7 


.235 


-0.2 


+0.6 


-5.2 . -5.6* 


n tt 


7 


.26 


-0.4 


+0.4 


-5.7 -6.6* 


tt tt 


9 


.20 


-0.9 


+0.2 


-3.3 


-4.0* 


tt tt 


11 


.12 


+0.1 


+0.4 


-1.0 


-1.8* 


tt tt 


13 


.125 


-0.4 


+ 0.1 


-1.1 


-1.7* 


tt tt 


15 


.14 


-0.9 


-0.1 


-1.5 


-1.9* 


No. 2 


3 


.20 


+4.0 


+4.5 


-8.3 


—7.9 


tt tt 


5 


.115 


+ 1.2 


+1.6 


-3.3 -2.9 


tt tt 


7 


.17 


+0.5 


+0.9 


-3.7 


-3.5* 


tt tt 


7 


.24 


—0.3 


fO.6 


—5.2 


-5.7* 


tt tt 


9 


.17 


-0.3 


+0.4 


-3.1 1 -3.1* 


tt tt 


11 


.12 


-0.3 


-rO.4 


-2.0 1 -1.7 ♦ 


tt tt 


13 


.12 


-0.4 


+0.1 


-1.1 -1.6* 


tt tt 


15 


.135 


-0.5 


0.0 


-1.4 -1.7* 

1 



Lloyd.^ 



Effect of Wave Form upon Transformers. 



503 



The generators producing the high frequencies do not give very 
high voltages. In order to use a high percentage of these, the 
generator supplying the fundamental frequency was excited to 
a correspondingly low voltage, and after combination the voltage 
was transformed up to the proper value. Transformer No. z was 

TABLE VIII. 



Per Cent Increase in Loss 



Transformer 


No. z 


No. 3 


No. a 


No. a 


No. 3 


No. 3 


No. 3 


m 


3 


3 


5 


7 


3 


5 


15 


h 


.18 


.20 


.115 


.23 


.165 
+4.4 


.115 


.41 


e= 0« 


+5.5 


+4.0 


+1.2 


-0.3 


+1.5 


-7.3 


30 


+5.7 


+4.2 




-0.1 


+4.7 




-7.0 


45 






+1.0 






+1.5 




60 


+4.8 


+3.2 




-0.6 


-4.0 
+2.0 




-7.0 


90 


+2.0 


+0.8 


-0.2 


-1.4 


+0.6 


-6.7 


120 


-1.6 


-1.9 




-2.3 


-1.0 




-7.0 


135 






—1.9 






-1.0 




150 


-5.1 


-5.6 




-3.7 


-4.2 




-7.2 


180 


-8.2 


-8.3 


-3.3 


-5.2 


-7.4 


-2.7 


-7.4 


210 


-8.1 


-8.0 




-5.1 


-7.6 


• 


-7.5 


225 






-2.1 






-3.0 




240 


-5.6 


-5.4 




-3.6 


-5.8 




-7.8 


270 


-2.3 


-2.3 


-0.5 


-2.5 


-2.7 


—1.2 


-7.8 


300 


+ 1.2 


+ 0.7 




-1.4 


+0.3 




-7.8 


315 






+ 0.7 






+ 0.5 




330 


+3.9 


+2.9 




—0.8 


+2.8 




—7.6 



used in this way with the results shown in Table IX. The volt- 
meter was connected to the primary side of the transformer. The 
calculated values for 5= 180° are obtained by the method given 
on p. 490. 

It will be noticed here that the experimental and the calculated 
values do not agree very well; indeed, the experimental results show 
very little effect from phase reversal. While seeking the reason for 
this, the effect of transforming the fundamental alone was tried. 



504 



Bulletin of the Bureau of Standards, \,voi. 4, no. 4. 



The iron losses were first determined by direct connection to the 
generator, then after transformation. With ratio of transformation 
1:2 the losses were 0.7 per cent less; with ratio 1:3 they were one per 
cent less than by direct connection. 

TABLE IX. 

Transformer No. a 





m 


h 




Increase in Loss 


Ratio of Pre- 
vious Transfor- 
mation. 


9- 


oo «-i8oo 




Exp. 


1 1 
Gale. Exp. Calc. 


1:2 


13 


.19 


-1.9 


-0.3 -2.3 \ -3.1* 


1:3 


13 


.27 


-4.0 


-1.5 -3.5 -4.2* 


1:2 


15 


.235 


-2.9 


-1.1 


-3.1 1 -3.2* 


1:3 


15 


.32 


-5.2 


-2.9* 


-4.9 -4.9* 


1:4 


15 


.44 


-8.4 


-6.0* 


—8.3 ' -8.1* 



Measurements were next made on Transformer No. 3, using the 
low-voltage winding as primary. In this way a large component 
of high harmonic could be used at a low voltage. Table X gives 
the results. 

TABLE X. 







/ 


Transformer No. 3 










m 
13 


h 


Increase in Loss in Per Cent 


Ratio of 
Transforma- 
tion 


9-0° 1 «<-z8o'' 

1 


tf-goP 




Exp. 


Calc. 1 Exp. 


Calc. 


Calc. 


60:120 


.17 


- 1.4 


-0.2 


- 2.3 


- 3.0* 


-1.6 


30 : 120 


13 


.36 


- 5.8 


-3.7* 


- 5.9 


- 7.2* 


-5.5* 


30 : 120 


13 


.48 


-10.4 


-7.9* 


-10.8 


—11.0* 


-9.5* 


60:120 


15 


.155 


- 1.2 


-0.2 


- 1.7 


- 2.4* 


-1.3 


30 : 120 


15 


.32 


- 4.5 


-3.3* 1 - 4.4 


- 5.7* 


-4.5* 



Table XI shows the effects of combining two harmonics with the 
fundamental. These harmonics were kept in the same phase rela- 
tion with each other, and both shifted with respect to the funda- 
mental, each shift amounting to 90° of the fundamental. The 
initial position was with the third harmonic in phase and the fifth 
harmonic reversed. 



uayd.] Effect of IVuve Form upon Transformers. 505 

TABLE XI. 



Tmnsformer No. a 
Two Harmonics 



mi =3 
mj=5 



hi =..1X3 
hi».xo9 



Phase Sotting 


Increase in Loss in Per Cent 


«i 


«t 


Exp. 


Calc. 


0° 


180^ 


-0.45 


+0.3 


180 





-3.5 


-2.6 


— 90 


- 90 


-0.6 


+0.8 


+ 90 


+ 90 


+ 1.9 


+0.8 


+135 


+ 45 


-1.1 


-0.8 


- 45 


-135 


+0.15 


+0.7 



Table XII presents a case where all of the generators were used 
together. The phase of each harmonic in this case was made either 
zero or i8o*^, and the amplitudes decreased as the frequency 
increased, so that mh was approximately constant and had the 
value 0.6. 

Table XIII gives the results of applying a large component of 
low harmonic to transformer No. 2. 

5. DISCUSSIOK OF THE RESULTS. 

Reference to Table VII discloses the fact that in the simple case 
of a single harmonic of small magnitude the experimental results 
agree with the theoretical values within one per cent When the 
higher harmonics enter in large proportion the agreement is not so 
good ; thus, with 20 per cent of the ninth harmonic the discrepancy 
for transformer No. i is i.i per cent. The loss with these higher 
harmonics in phase is always less than the calculated value ; when 
they are reversed in phase it is nearly always greater. This is even 
more apparent in Tables IX and X. In the latter there is very 
little difference between 5=o° and 5= 180°, the losses having the 
value which is about the mean of the calculated values, and which 
would apply to the case 5 =90°. 

In Table VIII and Fig. 7 it is seen that the maximum loss does 
not coincide with 6=^0^ nor the minimum with 5= 180*^, as indi- 
cated by the theory, but that the extreme values are for 5 =20° and 
5=200°, approximately. This can not be due to an error in the 
phase settings, since in the case of different harmonics different 



5o6 Bulletin of the Bureau of Standards, ivoi, /, no. 4. 

numbers of degrees of the fundamental correspond to 20° of the 
harmonic. The accuracy of setting of any generator is about 0.1° 
of arc, corresponding to 0.3° electrical in the fundamental, 4.5° 
electrical in the highest harmonic, and proportional values for the 
intermediate harmonics. The results point rather to a distortion of 
the wave between the generators and the transformer; that is to say, 
the wave form applied to magnetization is not the same as that sup- 
plied by the generators. This may be accounted for by the ohmic 
drop in leads, instruments, and primary winding. It is well known 
that, owing to the varying permeability of the iron, the wave of 
current has a different shape from the wave of emf.* The ohmic 
drop of potential, consequently, involves other harmonics and other 
magnitudes than the generator emf. Since the emf . used to magnet- 
ize the iron is the difference of these two, it also must have a wave 
shape different from the generator emf. When any considerable 
resistance is in the circuit, this effect becomes so marked as to give 
an entirely different wave. It is for this reason that no rheostat was 
used in the primary circuit, the current being controlled instead 
through the excitation of the generator. 

The fact that this effect is very noticeable is proven by the result 
obtained when an intermediate transformer was used, as compared 
with the losses obtained with direct connection to the generator. 
This amounted to one per cent with a sine curve for the original 
wave. 

With a large percentage of high harmonic the effect is even more 
marked, as illustrated in the last column of Table VIII. Here the 
maximum occurs at ^=270° and the minimum at ^=90°, and the 
range of variation is less than the theoretical value. By calcula- 
tion the extreme values for this case are -5.2 per cent and -7.3 per 
cent as against -6.7 per cent and -7.8 per cent experimentally. In 
all cases of a large component of high harmonic the calculation 
for 5=180° is based upon the modified formula given on p. 490, 

Q 

where 61 is taken as — - 

With a large component of lower harmonic the results given m 
Table XIII show an agreement with calculated values for 5= 180^ 
except in one case. Here the proper value for <^^ has been found by 

•Waves illustrating this are given by H. A. Pikler, Electrical World, 42, p. 218; 
1903. 



»o i 


,PER CENT INCREASE IN IRON LOSS 


o 










T 
1 
1 
1 
1 






\ 






o> 










1 

1 












o 










I 
\ 

1 
1 
1 
1 


1 
\ 1 


i 

1 
/ 
/ 


/ 






o» 




. 






1 

A. 


1 1 
1 1 


/ 
d t 


'/ 






o 










r 

1 
1 


1 

1 1 
1 1 
1 / , 


^ / 

/ / 
/ / 


/ 
f 
















1 


'7/ 


// 








o 




{ — 






f r 
/ / 
/ / , 
/ / • 


r/ 










^ - 




[ 




/ 


,'£i 












VI o 

'I 




^ 




A 








Itl^ttl 


2^ 








/y'/ 


f / 






z z z z z z z 








A' 


y / 


/ 






9 9 9 9 9 9 9 
(Ai a> o9 lo lo lo -^ 


S* >-* 






aV i 


V / 


/ 












t iSo 






f-o^ 


/ / 


1 












'/ / 


/ 
/ 


1 






-C i 


{ 


4 v ^ <l 


S z 




// / 


1 


/ / 


















/y / 


1 


/ / 


















'A / 


1 


/ / 














S s 


^ 


* \/ 


1 


/ / 














C OS 


tit 


V 


1 


]Jt Ji 












1 ' ' 


S zS 


F 


1 


f 
1 


/ 








S '^ 






1 


1/ 








-C J 


' 


» ♦ jfr <^ o 




1 




\ 














1 ' ! 




\ 




\ 
\ 


\ 

\ 












' 


s 2b; 


1 






\ 












o KS 




vTT 


\ 


i \ 














^ w 








\ \ 




% 










g: 






\ 
\ 


\> 














?• t 




N 


\ 


y\ 


\ 
\ 
\ 
















% 


\ \ 


\ 
\ 


















^ 


\ \ 

k 


\ 

\ 












fO 




, 




Nic 














O 








\ 




^N 




















V ' 


VoNi 










° 










\ 

\ 

\ 

\ 




\ 








w 










\ 
\ 
L 


\ 


\N 








o 










\ 

\ 
\ 

\ 


\ 

\ 
\ 


\ 








Ok 




I 






1 — ^ 


\ 

— nJb- 


\ 
\ 


\ \ 







507 



5o8 



Bulletin of the Bureau of Standards. 
TABLE XII. 



lVol.4,No.4. 



Tmnsformer No. 2 
Seven Harmonics 

hm— k— 0.6 ajpproximntely 
*»— ^4" ^6— ^e— *7 



in, -3 
mj-5 
m,-7 
m4-9 
me—iz 
m«-z3 



hi— .ao 
ht—.zo 
hs-.zo 
h4-.o8 

h«-.<«5 
hi -.045 



Phase Setting 


Increase in Loss in Per Cent 


«i 


«f 


H 


Exp. 


Calc. 


180° 


180° 


180° 


-7.8 


« 











+ 7.6 


+7.9 





180 


180 


-0.7 


« 


180 








-5.4 


—4.4 


180 





180 


-7.9 


# 





180 





+2.8 


+3.5 


180 


180 





-9.1 


« 








180 


42.2 


+2.2 



trial and used in the calculation. With 78.5 per cent of the third 
harmonic the secondary loops in the hysteresis curve become more 
pronounced and cover a range of induction of 14 per cent of B. 
This would increase the measured iron loss, and may well account 
for the discrepancy of 3.5 percent. 

For 5=0° the discrepancies between experimental and calculated 
values are more marked, amounting to three per cent. They are in 
the usual direction, the experimental loss being less than calculated. 
I know of no other cause for this than the distortion of the wave 
due to ohmic drop of potential, already mentioned. 

In the experiment with two harmonics the agreement is every- 
where within one and one-half per cent; the loss is smaller than 
expected, with one exception. 

In the experiment with seven harmonics the agreement is within 
one per cent in all cases where the formula can be expected to hold; 
that is, where 6=0^ for two of the lower harmonics. In the other 
cases <^i is not zero and would require a lengthy calculation for its 
determination. The discrepancy is always on the side of a lower 
loss than calculated. The loss is always less than with a sine curve 
unless the third harmonic is introduced in phase with the fimda- 
mental, in which case the wave will be flat or dimpled. 



Uoyd.] 



Effect of Wave Form upon Transformers. 
TABLE XIII. 



509 





h 


Increase in Loss in Per Cent 


m 


0- 


-o® 


0- 


x8o° 




Exp. 


Calc. 
-0.6 


Exp. 


Calc. 


3 


.785 


—3.6 


-22.1 


-25.6* 


5 


.605 


-7.1 


-3.8 


-14.2 


-15.0* 


5 


.39 


-1.6 


-4-0.6 


-10.1 


-10.3* 


5 


.32 


-0.4 


+ 1.3 


- 8.6 


- 8.8* 



It is apparent that transformer losses may be materially reduced 
by using an appropriate form of wave. When a generator is to be 
used primarily or principally to supply transformers whose load does 
not require a sine wave, it would be advantageous to design it with 
a wave form suitable for the accomplishment of this result. The 
desired result could be assured by the presence of a considerable 
component of the third harmonic in reversed phase, and suppressing 
as far as possible the higher harmonics, unless the phases of these 
can be controlled. This would give an unmistakably peaked wave. 

If the generator be three phase, three wire, it is not desirable to 
introduce the third or integral multiple of third harmonic. For, if 
star connected, the harmonic does not appear in the line voltage; 
if delta connected, a large short-circuit current of the triple fre- 
quency may circulate in the armature, wasting power.^ In this case 
it would be desirable to choose higher harmonics to produce the 
desired eflFect. These can be introduced by a suitable choice of 
armature teeth, not pushed to a too high flux density. In intro- 
ducing harmonics, however, it is always necessary to consider the 
danger from resonance. 

If the generator is to be used on a high tension line, the objection 
must be met that a peaked wave requires a higher maximum emf. 
for the same effective voltage, and consequently better insulation is 
required. While this argument carries some weight, it is sometimes 
overrated. The energy lost by leakage is independent of wave form. 

^This is discussed by C. P. Steimnetz, Trans. A. I. H. E., 25, p. 780; 1906: Elec- 
trician, 58, p. 573; 1907. 



5IO Bulletin of the Bureau of Standards, \voi. /, No. /. 

As for the breakdown of the insulation, it has been shown* that the 
steady voltage necessar}- for rupture may be greatly increased for a 
fraction of a cycle without breakdown. Furthermore, most break- 
downs on high voltage lines can be traced to surges of abnormal 
voltage due to some unusual condition, such as opening or closing a 
switch, not dependent upon the wave form, or to accidental reso- 
nance with some high harmonic. The insulation is liable at any 
time to be subjected to a stress due to twice the effective voltage.' 
It can not be taken for granted, consequently, that a peaked wave 
would require higher insulation than the same effective voltage in 
a sine wave. It would be advisable, however, to avoid high har- 
monics in the wave in order to lessen the danger from resonance 
effects. 

A greater objection to a peaked wave on long transmission lines 
is the fact that the high maximum emf. requires a larger charging 
current. How serious this feature of the case may be depends upon 
the constants of the particular line considered and the amount of 
power transmitted. 

If the secondary have an inductive load, so that its current and 
the corresponding component of primary current are not in phase 
with the emf., the difference in wave form due to the ohmic drop in 
potential will be accentuated, and the effect of the generator emf. 
upon the iron losses will be less certain. 

CONCLUSIOKS. 

With a given effective electromotive force the iron losses in a 
transformer depend upon the form factor of the emf, and vary 
inversely with it. 

With a given form of wave, the effect upon the iron losses may 
be computed approximately from the formulae derived, providing 
the higher harmonics are not prominent. 

By proper design of the generator supplying transformers, the 
iron losses may be reduced to a minimum, 

Washington, Oct. 31, 1907. 

^ C. Kinzbrunner, Electrician, 55, p. 809; 1905. 

• P. H. Thomas, A. I. E. E. Trans., 24, p. 317; 1905. 



THE LUMINOUS PROPERTIES OF ELECTRICALLY 
CONDUCTING HEUUM GAS. 



P. G. Nutdng. 



mXRODUCTION. 



A gas conducting an electric current radiates the energy imparted 
to it by the current. Neglecting relatively very slight losses due to 
conduction and convection, the efficiency of such a gas as a trans- 
former of energy from electrical energy into radiation should be a 
constant approaching unity in value. Radiation from a gas should 
then be expressible in terms of current and other specificable condi- 
tions with considerable precision. To express this radiation in 
terms of light, the spectral distribution of the radiation and the 
visual sensibility of the observer must be known. Upon the con- 
stancy of these latter depends the constancy of the relation of light 
to current. 

The results here presented relate to the amount of light per unit 
length emitted laterally by a column of helium gas carrying a 
known current The chief object of the investigation was to deter- 
mine the constancy and reproducibility of such a source of light 
and the specifications most favorable to constancy and reproduci- 
bility. The variation of light emitted with current, potential grad- 
ient, gas density, frequency of alternation of current, orientation of 
tube, with diameter of capillary and with time were studied in turn. 

Conducting helium emits light of a yellowish white color better 

for photometric comparisons with a glow lamp than that from any 

other of the permanent gases. Next best is, perhaps, carbon dioxide. 

This emits a snow-white light, but decomposes and disappears rap- 

22832 — 08 4 511 



512 Bulletin of the Bureau of Standards. {voi. /, No. 4. 

idly, with but moderate current densities. Sulphur vapor emits 
bluish-white light, but its density is difficult to measure and control. 
Helium has the further great advantage of not disappearing rapidly 
as other gases do when conducting a heavy current. The life of a 
tube of helium is at least fifty hours as compared with half an hour 
for a similar tube of hydrogen or nitrogen carrying the same current. 
Preliminary tests with tubes of various forms led to the adoption 
of a simple straight form with disk electrodes. The electrodes are 
of aluminum 1.5 mm thick and 25 mm diameter in spherical bulbs 




Pig. I. 

35 mm in diameter. These bulbs are connected by a straight piece 
of capillary tubing 50 mm in length and 2 mm in internal diameter. 
Foil 5 mm wide was wound about either end of the capillary to give 
the light emitting portion a definite measurable length. Light 
from the bulbs was screened off from the photometer. 

2. METHOD OF PREPARING TUBES. 

Ordinary methods were used in filling except that extra precau- 
tions were taken to free the electrodes from hydrogen. The tubes 
were cleaned with chromic acid and water and exhausted with a 
Geryk oil pump. After from twenty minutes to an hour of steady 
pumping with heavy current running through the tube, the last 
trace of hydrogen disappeared. Then helium was admitted, its 
pressure adjusted to about 5 mm and measured by means of an oil 
manometer of special design and the tube sealed off. The apparatus 
used in filling the tubes with pure helium at the proper pressure is 
shown in Fig. 2. Four very carefully ground stopcocks of 3 or 4 
mm bore are joined in a line about 10 cm apart. The outer end of 
the first is fitted with a ground joint for attaching to the pump. 



NuUinf.'] 



Luminous Properties of Helium Gas. 



513 



Between the first and second is attached a small auxiliary Plucker 
tube to aid in adjusting the pressure and testing the vacuum. 
Between the second and third cocks is attached an oil manometer 
of special design and a branch for attaching and sealing off the 
tubes to be filled. The space between the third and fourth cocks 
serves as an auxiliary reservoir in admitting helium and protects 
the open helium bulb in case the apparatus remains idle for a con- 
siderable time. Beyond the fourth cock is a piece of large tubing 
to which the bulb of helium is cemented. 

The sealed bulb containing helium must be opened without 
exposing the helium to contact with rubber tubing, water, or mer- 
cury. To accomplish this a massive piece of glass rod or capillary 




Fig. 2. 

(metals contain too much absorbed gas) is cemented to the end of one 
tip and the neck of the tip scratched for breaking. The whole tip 
and weight is then inserted in the large tubing projecting beyond 
the fourth stopcock and the bulb back of the tip cemented, as shown, 
to this tubing with a fusible cement (rubber dissolved in resin and 
boiled in a vacuum). After the apparatus has been exhausted to a 
nonconducting vacuum for several days, a sharp tap will crack off 
the tip of the helium bulb and liberate the gas. A reservoir opened 
in this manner may be drawn from for months without contamination. 
The stopcocks should be greased with a solution of natural rubber 
in vaseline that has been freed from absorbed air by boiling in a 



514 Bulletin of the Bureau of Standards. \via.4sNo.4. 

vacuum just before using; all four stopcocks should be rotated at 
intervals during exhaustion. 

The oil manometer was filled with the oil ("standard gas engine") 
used in the Geryk air pump. This oil is about one-fifteenth the 
density of mercury, so that pressure readings are greatly enlarged. 
It was vacuum boiled before using. Since this oil, like so many 
other similar hydrocarbons, rapidly absorbs air and other gases, it 
was necessary to make the manometer self-exhausting as shown. 
The stopcock is left open except when a reading is to be taken. 
A mercury manometer or McLeod gauge could not be used for 
measuring the pressure of the helium gas without too great con- 
tamination. The vapor pressure of this oil is below that of a non- 
conducting vacuum except in the warmest summer weather, and 
then a cold-water jacket is easily applied to both manometer and 
pump cylinder. 

In filling standard tubes with helium the greatest difficulty is in 
freeing the electrodes from hydrogen. This is best accomplished 
by steady pumping while a heavy current is passing through the 
tube. After but a few minutes pumping nearly all of the im- 
purities except hydrogen will disappear, indicating, perhaps, that 
the interior walls are clear of gas. After about fifteen minutes fur- 
ther pumping the hydrogen pressure drops abruptly. This, I take 
it, is when the disk portions of the electrodes are depleted of included 
hydrogen. To completely clear the stems of the electrodes requires 
further pumping and current for perhaps an hour. No air or helium 
should be admitted during this process, as it makes the complete 
elimination of the hydrogen much more tedious and difficult. 

After the tube refuses to conduct even a 5000-volt current, helium 
may be admitted. This usually shows impurities (probably atom- 
ized stopcock grease), but these are easily removed by the pump. 
After two or three fillings, the tube should show only the pure 
helium spectrum, without a trace of the red hydrogen line, and may 
be sealed off. 

Various other methods of eliminating traces of hydrogen were 
tried — oxidation and removal as water vapor, absorption by an 
auxiliary electrode of sodium-potassium alloy, absorption by cold 



Nutting:.] 



Luminous Properties of Helium Gas, 



515 



palladium and hot calcium and absorption by charcoal in liquid 
air — ^but none were found entirely effective. 

The purity of helium may be readily judged without a spectro- 
scope by the color of the cathode glow. In pure helium this is of 
a clear magenta tint, but if there is a mere trace of impurity present, 
this is lost 

The tubes were operated on a 5000-volt alternating current from 
a transformer controlled by resistance in its primary. The light 
emitted was compared with that from a calibrated 4-candle glow 
lamp by means of a Lummer-Brodhun photometer of the equality 
type. The uncertainty in each determination is about two per cent, 
the probable error less than one per cent. In a spectrophotometric 
comparison, the uncertainty would have been from 10 to 100 per 
cent on account of the variable line width. 

3. VARIATION OF LIGHT WITH CXTRRENT. 

The variation of light with current in various forms of tube is 
shown in the accompanying tables and curves. The light from the 
whole capillary taken with the tube stationary is given in candles, 
but is uncorrected for mean horizontal. 



Tube 


Current in Milliamperes 


No. 


zo 


X5 


ao 
1.19 


as 


30 


35 


40 


45 


18 


0.58 


0.94 


1.33 


1.39 


1.42 






27 


0.55 


0.86 


1.16 


1.45 


1.71 


1.92 


2.11 


2.30 


43 


0.29 


0.68 


0.96 


1.23 


1.47 


1.69 


1.89 


2.09 


39 


0.60 


0.92 


1.23 


1.54 


1.83 


2.06 


2.30 


2.53 



The dimensions of these tubes are : 

No. 18. Capillary i. 2 mm diameter, 40 mm long. 
<( 2^ .« J 8 " " 54 ** 

4. 29. '« 2.17 ** '• 49 '* 



5i6 



Bulletin of the Bureau of Standards. 



[yol.4.No.4. 



The plotted curves indicate the effect of size of capillary. Tube 
No. 1 8 with its small bore gives a curve much steeper at the start, 



2.0 



111 



X 
i3 

3 




10 



20 30 

CURRENT (MILLIAMPERES) 
Fig. 3. 



^ 



but early approaching a maximum. Tubes of larger bore give 
curves of less curvature. 

More precise corrected values for the variation of light with 
current obtained later are given below. 



Current (Mllliamperes) 



22 

23 
24 
25 

26 
27 
28 



Correction to Candle Powrer per cm Length of 
Capillary 



+0.0387 
+0.0258 
+0.0136 

0.0 
—0.0130 
—0.0256 
—0.0376 



Nutting.] 



Luminous Properties of Helium Gas. 



517 



4. VARIATION OF LIGHT WITH POTENTIAL GRADIENT. 

The variation of light with potential gradient was studied with 
the purpose of expressing light emitted in terms of energy absorbed. 
Auxiliary potential electrodes of platinum wire were inserted at 
each end of the capillary portion of the tubes and potential readings 
taken with a multicellular voltmeter. It was found that fairly con- 
stant potential readings could be obtained. It was found, however, 
that by playing a flame or blast of cold air upon the capillary a 
variation of five or ten per cent in the indicated fall of potential 
could be produced. This variation, however, was not accompanied 
by a variation in the light emitted so long as tKe current was held 
constant 

Some typical data is given in the following tables and curves : 

Variation of Potential Gradient with Current 

I. Tube No. 38. CapUlary 2.17 mm diam., 50 mm long, Pressure 4.2 mm 
II. " •* 43. " 3.12 '* ** 50 " '' " 5.0 " 



Current 
(milliamperes) 


Light 
(candle) 


P. Q. (volts) 


Energy 

(watte) 


Candle 
Watt 


Watts 
Candle 




10 


0.60 


274 


2.74 


0.219 


4.57 




15 


0.86 


256 


3.84 


0.227 


4.40 




20 


1.21 


245 


4.90 


0.246 


4.07 


(I) 


25 
30 


1.50 
1.76 


237 
233 


5.92 
6.99 


0.253 
0.258 


3.96 
3.88 




35 


2.00 


231 


8.10 


0.247 


4.05 




40 


2.24 


230 


9.20 


0.244 


4.11 




45 


2.46 


229 


10.30 


0.239 


4.19 




10 


0.39 


233 


2.33 


0.169 


5.92 




15 


0.68 


211 


3.16 


0.215 


4.65 




20 


0.96 


198 


3.96 


0.242 


4.14 




25 


1.23 


190 


4.75 


0.259 


3.88 


(11) 


30 


1.47 


185 


5.55 


0.265 


3.78 




35 


1.69 


180 


6.30 


0.268 


3.74 




40 


1.89 


176 


7.04 


0.268 


3.74 




45 


2.09 


173 


7.79 


0.268 


3.74 




50 


2.28 


170 


8.50 


0.268 


3.74 



5i8 



Bulletin of the Bureau of Standards. 



[Vol. 4. No. 4. 



The two curves for fall of potential plotted against current are 
of the typical form for the anode column of a conducting gas. 
That for the larger capillary is lower and on a larger scale. These 
curves are of very nearly the same form for all pressures from 2 mm 



280 



260 



CL 

s 



240 



UJ 

g«0 



200 



180 



160 




10 



20 



30 



CURRENT 
Fig. 4. 



40 



to 10 mm, but are a few per cent higher at the higher pressures. If 
the auxiliary' electrodes took up the actual potential of the gas, the 
above data gives an indication of the luminous efficiency of such a 
tube. It passes through a maximum at a current density of about 
6 milliamperes per square millimeter. The low luminous efficiency 
of helium is largely due to the three infra-red lines at 728, 11 17, 
and 2040 /i/A which represent at least 90 per cent of the radiation 
without contributing to the light emitted. 

5. VARIATION OF LIGHT WITH GAS DENSITY. 

The variation of light emitted with density of gas was studied by 
means of tubes of three different diameters filled with helium at 
pressures ranging from 2 mm to 10 mm and carrying currents of 10 
to 45 m.a. Gas pressure was measured on a special manometer con- 
taining gas-free pump oil of one-fifteenth the density of mercury. 



Nutting.] 



Luminous Properties of Helium Gas. 



519 



Each tube was first filled with pure gas at the highest pressure, then 
the pressure reduced in steps by temporarily connecting with a 
highly exhausted auxiliary bulb of proper size. 

Variation of Light with Gas Density, 

Tube No. 43. Capillary 3.12 mm diam., 50 mm long 



Oaa Pressare In mm Hg. 



Current 


8.5 


6.6 


5.0 


3-7 


a.5 


10 


0.13 


0.26 


0.41 


0.42 


0.33 


15 


0.34 


0.52 


0.71 


0.75 


0.65 


20 


0.53 


0.82 


1.01 


1.03 


0.92 


25 


0.74 


1.09 


1.29 


1.34 


1.20 


30 


0.92 


1.31 


1.54 


1.58 


1.53 


35 


1.11 


1.60 


1.77 


1.79 




40 


1.31 


1.71 


1.98 


1.99 




45 


1.46 


2.01 


2.20 


2.07 




50 




2.12 


2.40 


2.17 





2.0 



ui 

o 



z 



1.0 




10 MA 



4 5 6 

PRESSURE (M M) 



10 



Fig. 5. 



520 Bulletin of the Bureau of Standards. \voi.4,so.4. 

Tube No. 38. Capillary 2.17 mm diam., 50 mm long 

Qas Pressure 



Current 


9.0 


7.7 


5.8 


4.a 


a.8 


X.9 


10 


0.38 


0.55 


0.55 


0.55 


0.48 


0.08 


15 


0.70 


0.87 


0.91 


0.90 


0.83 


0.66 


20 


0.98 


1.22 


1.24 


1.24 


1.20 


0.91 


25 


1.25 


1.51 


1.54 


1.54 


1.54 


1.24 


30 


1.48 


1.79 


1.83 


1.85 


1.86 


1.51 


35 


1.72 


1.99 


2.10 


2.10 


2.10 


1.71 


40 


1.96 


2.20 


2.31 


2.35 


2.07 




45 


2.11 


2.35 


2.47 


2.56 


2.58 





Tube No. 45. Capillary 1.03 nrni diam.» 50 mm long 



Gas Pressure 



Current 


Z0.0 


6.x 


4.8 


10 


0.47 


0.45 


0.44 


15 


0.25 


0.67 


0.66 


20 


0.93 


0.89 


0.86 


25 


1.12 


1.08 


1.07 


30 


1.25 


1.21 


1.19 


35 


1.33 


1.33 





The complete data on Tube No. 38 is reproduced in Fig. 5 with 
one curve dotted for each of Tubes 43 and 45. The curves for the 
2-mm tube parallel the pressure axis over a wide range of pressure 
and current. For the 3-mm capillary the curves are higher at lo^'er 
pressures, for the i-mm capillary at high pressures. 

6. USE OF DIRECT AND ALTERNATING CURRENT. 

The form of current was varied from direct to alternating of high 
and low frequency and voltage without disturbing the apparatus. 
The direct looovolt current from two 500-volt generators in series 
could be controlled at 22.5 m.a. and 23.7 m.a. Afterwards the 



JVmUing^.] 



Luminous Properties of Helium Gas, 



521 



more easily adjustable alternating current was brought to these 
values. The data taken is as follows : 



Form of Current 



Light Emitted 



Current = aa.5 m.a. 33.7 m.a. 



Direct current, 1000 volts 

Alternating 'S 5000 YOlts, 60 cycles 
" ", 5000 volts, 900 " 

*' ", 2000 volts, 60 " 



1.21 
1.22 
1.21 
1.22 



1.30 
1.29 
1.29 
1.28 



The slight differences observed are less than the uncertainty in 
the light determinations. 

7. VARIATION OP LIGHT WITH ORIENTATION OF TUBE. 

The light emitted by a tube varies with its orientation on account 
of irregularities in the capillary. Heavy-walled capillary is worst, 
deviations of ten per cent from the mean horizontal being not 
uncommon. Walls i mm thick are sufficiently strong for such 
tubes, and such thin-walled capillary, if carefully selected, is found 
to give deviations of but one or two per cent from the mean. Such 
deviations are of slight consequence when the mean horizontal is 
obtained. 

8. VARIATION OF LIGHT WITH CURRENT DENSITY. 

The diameter of the capillary affects the light emitted per cm 
with a given current. Tests of saturation indicated that in such a 
luminous column of gas practically all the radiation comes from 
within half a millimeter of the surface, so that light emitted would 
vary with the area of longitudinal section rather than with volume. 
Current density varies inversely as the square of the diameter, so 
that if the light varied directly as the diameter (at constant current 
density), as above indicated, it should vary approximately inversely 
as the diameter at constant current. Data is available on four dif- 
ferent diameters of capillary at 25 milliamperes of current: 

Diameter of capillary 1.029 1.949 2. 168 3. 12 mm 

Mean horizontal candle power per cm at 25 m.a .. . 0.365 0.325 0.31 1 0.259 



522 



Bulletin of the Bureau of Standards. 



\Vol.4.So.4. 



These four points lie near a smooth curve that is nearly a straight 
line. 

In the light of the above results, the specifications most suitable 
for constancy and reproducibility in a helium standard of light 
intensity may be drawn up, namely, a current of 25 milliamperes, a 
capillary of 2 mm diameter, and a gas pressure of about 5 mm, which 
need not be accurately known. Conversely it might be stated that 
a tube having a capillary of 2 mm bore, filled with pure helium at 
5 mm pressure, will emit N mean horizontal candles per centimeter 
of length when carrying a current of 25 milliamperes. The con- 
stant N has been shown to be very nearly if not quite independent 
of other small variations. The uncertainty in the value of N, aside 
from the uncertainty in its photometric determination, is very small, 
probably much less than one per cent. 

To test reproducibility, a set of six duplicate tubes were made up 
with capillary 2.168 mm in mean internal diameter and filled at 5 
mm pressure. These gave the following values in mean horizontal 
candles per cm length at 25 milliamperes: 



Tube No. 


Light per cm. 


Deviation from mean. 




37 


0.325 


-0.003 




38 


0.329 


+0.001 




39 


0.332 


+0.004 




40 


0.328 


0.000 




41 


0.326 


—0.002 




42 


0.326 


-0.002 






Mean 0.328 


0.002 






±0.001 







The greatest deviation is only about a per cent, the average devi- 
ation less than a per cent, and the probable error in the mean value 
less than one-third of one per cent 

The correction for bore of capillary is 0.009 from the curve of 
variation of light with bore, so that this set of tubes gives the value 
of the constant N, 0.337 candle per centimeter. 



Nmtiing.] Luminous Properties of Helium Gas. 523 

9. VARIATION OF LIGHT WITH TIME. 

Incidentally, many tests for a time efEect were made. At the end 
of a long series of observations with varying current or orientation, 
tubes would be brought back to the initial current or position and 
their light values checked with previous ones made half an hour 
before, and these with others made a week or a month previously. 
In every case values checked up to within the uncertainty of obser- 
vation. In the few cases where apparent changes were recorded the 
change was large and due to an obvious change in the tube itself, a 
crack or the development of hydrogen or a cathode deposit due to 
current overload. 

10. OONCLUSION. 

These results are so promising that the helium tube seems to me 
to be worthy of consideration as a primary light standard. Its free- 
dom from the troublesome atmospheric corrections to which the 
Hefner, Carcel, and pentane standards are subject is very much in 
its favor. The only quantity to be measured while in operation is 
the current, and this may easily be determined with the required 
precision. 

The uncertainties in the value of the light constant N are of three 
classes, and these require further investigation before the helium 
tube may be considered as a competitor of existing standards. These 
uncertainties are: 

1. Those in the separate determinations of the same observer on 
the same tube. These are not serious, being of the same order as 
the uncertainties in ordinary' photometric work. 

2. Uncertainties due to using different tubes. Reproducibility 
will require further investigation with capillaries of different kinds 
of glass and of different diameters. If this uncertainty is no greater 
than is indicated by the test of the six tubes, 37 to 42, above re- 
corded, it is of little consequence. 

3. Uncertainties due to varying the observer on account of color 
differences. These are the most serious of all, and require careful 
investigation by many different observers. 

Washington, December, 1907. 



FUNCTION OF A PERIODIC VARIABLE GIVEN BY THE 
STEADY READING OF AN INSTRUMENT; WITH A 
NOTE ON THE USE OF THE CAPILLARY ELECTROM- 
ETER WITH ALTERNATING VOLTAGES. 



By Morton G. Uoyd. 



This investigation was made in the hope of finding an instrument 
which would register the average (numerical) value of an alternating 
electromotive force, but an examination of the conditions shows 
that no instrument can answer this purpose unless its deflection is 
independent of the direction of the applied voltage and proportional 
to that voltage in numerical magnitude. 

In instruments whose parts have relative motion, as a gal- 
vanometer, the force exerted depends upon the position of the moving 
part and upon the variable being measured, which for brevity will 
be referred to as the voltage. In others, such as the Siemens 
dynamometer or the capillary electrometer with uniform bore (or in 
which the hydrostatic pressure is varied to keep the meniscus 
stationary), the force depends upon the voltage alone. 

In either case, if the moving part maintains a fixed position dur- 
ing the variations of the voltage, the variations of force during a 
period depend only upon the variations of the voltage, and the aver- 
age value of that force is what determines the deflection and is 
measured by it. The function given by the instrument reading 
consequently depends only upon the law of force involved. Let us 
suppose that the force is such a function of the voltage that it may 
be expressed by a series of powers. 

F=^A,+A,e+A^^A^^-^ 

525 



526 Bulletin of the Bureau of Standards. \voL4.so.4. 

The average value of the force during a period, 7", is 

edt+-j^ I e^dt+ 



Fdt=A,+-^ I edt+j^ I . 



The terms involving odd powers of e disappear, for 



' <?"<//= — I e^di and hence I 






when m is an odd int^^r. 

Since A^ is the force corresponding to the zero reading, we have 
for the force due to the voltage 

e^dt+"^ I e'dt+ 






and it is evidently impossible that the instrument should indicate 
the average value of the voltage. 

Let us consider the relation between deflection and voltage to be 
parabolic, as is approximately the case with the capillary- electrom- 
eter, so that 

D=b^ -,{e^a)^=2-e^~e^ 
a*^ ' a a^ 

where b is the maximum positive value of Z>, occurring when e—a, 
(See Fig. i.) Then since the law of force is here the same as the 



where 






F-A^=-4=. I ^dt= - A^ 






law of deflection and may be designated the effective value of e. 



Uoyd] 



Function of Variable Read by an Instrument, 



527 



The deflection in this case is always negative and follows a para- 
bolic law of variation with E^ in approximate agreement with the 
experimental results (see p. 529). 

An instrument can only give readings proportional to the numer- 
ical average value of e by having the coefficient A^ change sign with 
^, and A^—0=A^^ etc. This can be accomplished in two ways; 
first, by reversal of the force at the instant e is passing through the 
value zero; secondly, by making the permanent factor in the deflect- 
ing force controlled as to direction by the variable factor. The first 




Fig. 1. 



method has been applied in an apparatus already described in this 
Bulletin,^ The second method is difficult of application, but a 
hypothetical case may be mentioned by way of illustration. 

Let the moving element in the instrument be a soft iron needle 
surrounded by a coil of wire of sufficient turns, so that the smallest 
current to be measured — in fact, a small percentage of its maximum 
value — ^will magnetize it to saturation. Let the current to be 
measured traverse also a coil so placed that its field will deflect 
the magnetized needle. Then the torque acting on the needle will 
be constant in direction and proportional to the current Besides 

* Lloyd and Fisher, Bull. 4, p. 467; 1908, where a rotating commutator in syn- 
chronism with an A. C. generator is used. 
22832—08 5 



528 Bulletin of the Bureau of Standards. \voi. 4. N9. 4. 

being impracticable on account of the prohibitive inductance nec- 
essary, this scheme is open to certain theoretical objections, but it 
will serve as an illustration of the necessities of the case. 

Dynamometer ammeters for alternating currents have been 
devised" in which the deflection is proportional to the current, since 
by the positions of the coils the force is made to vary inversely as 
the deflection. 

It may seem at first sight as though the indication of such an 
instrument would depend upon the average value of the current, 
but it has been shown above that it would depend upon the effective 
value. The reason for this is, that it is the force which is inte- 
grated, and the deflection is determined by the average value of the 
force, and not by the average value of the deflections which would 
result if the variable were to proceed very*^ slowly through a cycle. 

If Z> be the deflection, i the instantaneous current, /^= k^ _ and 
since the controlling force is proportional to the deflection, we have 

dJ^^ ^pV/, or D^z^k^I 

where / is the effective value of the current. 

"H. Bruger, Phys. Zs., 4, p. 876; 1903. 



ON THE USE OF THE CAPILLART SLECTKOMETBR WITH ALTERllATDrG 

VOLTAGES. 

The capillary electrometer, introduced by Lippmann' in 1873, has 
been used extensively by physiologists and physical chemists,* and 
more lately has received attention as a laboratory instrument for 
more general use.' 

This form of electrometer has been used more generally as a null 
instrument, but can also be used for deflections, if the scale be cali- 
brated. Calibration is necessary, since except for very small ranges 
the deflection is not proportional to the applied voltage. When used 
as a deflecting instrument, the mercury in the capillary is usually 
charged negatively and the electrolyte positively, but this is not 
necessary, as deflections can be obtained in either direction. 

So far as is known to the author, the instrument has never here- 
tofore been used with alternating potentials, except in the wave- 
tracing experiments of Burch. His instrument was designed to 
have short period and to be dead beat, and very low voltages were 
used. 

If a curve be plotted between deflections and applied direct volt- 
ages, it has the general form of a parabola, as shown in Fig. 3. 

It was surmised from this that the instrument would respond to 
an alternating voltage with a deflection, and such was found to be 
the case. 

The electrometer was set up, as shown in Fig. 2, the beaker 
having a layer of mercury at the bottom covered with the electro- 
lyte. A glass tube was drawn to a capillary and bent as shown, 
then partly filled with mercury and the capillary end immersed in 
the electrolyte. Platinum wires dipping into the mercury formed 
the electrodes, and were protected from contact with the electrolyte. 
A micrometer microscope was focussed upon the surface separating 

'G. Lipptnann, Pogg. Ann., 149, p. 54^; 1873. 

*W. Ostwald, Zs. f. Phys. Chem., 1, p. 404; 1887, and Ostwald and Luther's 
Fhysiko-chemische Messungen, 2te Auflage, p. 333. 
•G. J. Burch, London Electrician, 87, p. 380; 1896. 

C. F. Burgess, Trans. A. I. E. E., 16, p. 337; 1898. 

A. D. Cole, Bull. Scientific Lab. Denison Univ., 11, p. 265; 1902. 

A. W. Vining, Ann. chim. phys., 9, p. 272; 1906. 

529 



530 



Bulletin of the Bureau of Standards. 



\Vol.4,No.4. 



the two liquids in the capillary, and any change in the position of 
the meniscus due to electrification could be measured. 




rig. 2. 

The electrolyte used was an aqueous solution of sodium chloride. 
This was chosen as less likely to gas at low voltages than sulphuric 
acid, the electrolyte usually employed/ The diameter of bore at 
the surface of separation was about 0.7 millimeter. A finer bore 
was avoided in order to lessen trouble in case of gassing. 

•F. Paschen, Wied. Ann., 39, p. 43 ; 1890. 



Ucyd.] 



Capillary Electrometer. 



531 

















































/ 


^ ' 








""^ 


\ 


















> 


/ 












\ 














300 




/ 
















\ 


V 














/ 


















\ 










300 


/ 




















\ 


\ 










/ 






















\ 








^ IfMI 


/ 






















\ 








.WW 


/ 
























\ 






s. 


/ 





2 





4 





6 





8 


1 


vo 


-TS 1 


A 


1 


4 






^^ 






















\ 








— 1W 








"^ 


^ 


^ 












— \ 


\ 






















^ 










\ 




1 


— 9110 


























\ 
































\ 





































































































































































Fig. 3. 



532 Bulletin of the Bureau of Standards, [^01.4,^0,4. 

The electrometer was first calibrated with direct voltage, and the 
results are shown graphically in Fig. 3, curve D. C. Alternating 
voltages were next applied, with the results shown in curve A. C, 
whose abscissae are effective volts, as read upon a dynamometer. 
Direct voltages are considered positive when the mercury in the 
capillary is connected to the negative pole of the battery. With 
direct voltages the position of the meniscus was perfectly definite 
and reproducible. With alternating voltages the readings, except 
for very small voltage, are not steady and are not reproducible. 
The set given in the figure is simply a sample of their general value. 
On account of this uncertainty in deflection the electrometer could 
not be used for an accurate measiurement of alternating voltage. 
This difficulty is probably due to the fact that the surface never 
comes to rest, but a photographic record would be necessary to 
detect the motion. 

As a detector of alternating voltages, it would be perfectly feasible 
to use the electrometer. The sensibility, however, is very much 
smaller for A. C. than for D. C. on the same instrument, and it does 
not maintain its advantages in this field of work. In an age when 
a telephone is a universal laboratory instrument, the electrometer can 
hardly be expected to attain very general use. There are two fea- 
tures of this instrument, however, which should be kept in mind 
with regard to its use for both direct and alternating voltages. These 
are the fact that it is an electrostatic instrument, requiring only suffi- 
cient current to charge or polarize it, and its cheapness. In many 
laboratories where the cost of more elaborate apparatus is prohibitive, 
the capillary electrometer may be made to answer many purposes. 

Washington, December 30, 1907. 



SELECTIVE RADIATION FROM THE NERNST GLOWER. 



By W. W. CoUcntz. 



INTRODUCTION. 

The measurement of very high temperatures is based upon an 
extrapolation of the laws governing the energy emitted by a body 
with change in temperature. Our knowledge of these laws is cx)n- 
fined to the radiation from platinum and from a hollow inclosure 
(so-called "black body"), which is the nearest approach to a com- 
plete radiator. The remarkable progpress that has been made in 
the development of processes requiring an accurate knowledge of the 
temperatures involved makes it imperative to study the laws of radia- 
tion of various substances with variation in temperature. In order 
to determine these radiation laws, it is generally necessary to study 
the spectral energy curves, using for the purpose a prism that is 
transparent to heat rays and some sort of very sensitive heat measur- 
ing device, such as, for example, a bolometer or a thermopile. It is 
also possible to study the total radiation emitted. The chief diflB- 
culty in establishing the so-called radiation constants of substances 
lies in determining the exact temperature of the radiating surface. 

The distribution of radiant energy in the normal spectrum of all 
solid bodies thus far studied is unsymmetrical about the maximum 
of the energy curve, having the appearance of a probability function 
modified by suitable constants. The solids heretofore studied,* in 
which it was possible to determine the approximate temperature, 
have spectral energy curves, which are represented fairly well by the 
function, 
(i) E=c,\-''e-'*''^ 

*Paschen, Ann. der Phys., (3) 68, p. 455; 00, p. 663; 1897; (4) 4, p, 277; 1901. 
Lummerand Pringsheim, Verh. d. Deutsche Phys. GeseU., 1, p. 215; 1899. 

533 



534 Bulletin of the Bureau of Standards, {yoi,4.No,4. 

In the case of the complete radiator, or so-called black body, the 
exponent « = 5, while for platinum, a = 6. 

In order to determine the constants of the above equation from 
the spectral energy curves, it is necessary to know the temperature 
of the radiator. Fortunately the exponent, a, may also be obtained 
from the spectral energy curve in which the temperature, 7", is con- 
stant without knowing the actual temperature, for it can be shown 
from eq (i) that the ratio of the emissivities (the observed bolometer- 
galvanometer deflections) for any two wave-lengths X and Xtnax^ is: 






\nax ^ 
\ 



e 



from which a may be determined. It was found by Paschen, that 
for carbon, platinum, etc., the value of a obtained in this way was 
in agpreement with that obtained from a knowledge of the tempera- 
ture of the radiator. 

With this -equation it is possible to obtain some idea of the 
probable total emissivity of a radiating body, as to whether it is pro- 
portional to the 4th power («— i =4 for a black body, a— i = 5 for 
platinum) or to some higher power of the absolute temperature. 

Of course the assumption is made that the emissivity function is 
similar to that of platinum and of a black body. How far this 
assumption falls short of the observed facts is brought out in the 
present paper, in which it is shown that the observed radiation 
curve of a Nemst filament, which at high temperature gives an 
apparently continuous spectrum, is in reality the composite of 
numerous sharp emission bands, which increase in intensity and 
broaden out with rise in temperature. 

The constant a for various substances has not been extensively 
investigated, and it is purposed in this, and in subsequent reports, 
to state the results of a study of various substances (including incan- 
descent filaments) together with the redetermination of the con- 
stants of a complete radiator, or so-called black body. 

The study of the metal lamp filaments is of interest in connection 
with the speculations as to whether the great light emissivity (high 



CobUntx,) Selective Radiation from the Nernst Glower. 535 

luminous efficiency) is due to an abnormal emission in the visible 
spectrum, with a corresponding suppression of the radiation in the 
infra-red, or whether the effect is due to the high temperature at 
which the lamp is burning. In the latter case the distribution of 
energy in the spectnim may be uniform (no discontinuities), but a 
larger portion of it will lie in the visible spectrum than at low tem- 
peratures. From a theoretical consideration of the fact that the 
filaments are metallic, electrical conductors with a high reflecting 
power in the visible, and probably reflecting uniformly high in the 
infra-red,* one would expect the distribution of energy in the spec- 
trum to follow a law similar to that of platinum, but with dif- 
ferent constants. The results obtained thus far from a study of such 
metals as tungsten and osmium support this hypothesis. On the 
other hand, in the case of oxides, which conduct electrolytically at 
high temperatures, there is not sufficient data from which to form even 
a working hypothesis. All of the oxides thus far examined have no 
strong absorption bands near the visible spectrum; the only excep- 
tions being the oxides of the rare earths, such as cerium, thorium, 
lanthanum, didymium, erbium, etc., the compounds of which have 
strong, sharply defined absorption bands in the visible spectrum, and 
at least some of these have absorption bands in the infra-red. A 
low reflecting power seems to be characteristic of the oxides (like 
transparent media, electrical nonconductors) throughout the infra- 
red to about 8ft, beyond which point they have strong bands of 
selective reflection. In this region the emission will be suppressed 
in proportion to the reflecting power. ' In the rest of the spectrum 
the emission will be proportional to the absorbing power (general 
absorption), while at the point where there is a band of selective 
absorption in the transmission spectrum there will be an emission 
band in the emission spectrum, provided the radiation is a purely 
thermal one, following Kirchhoff's Law. 

In the case of the Auer mantle the emission spectrum is a series 
of emission bands at i to 2/x, with practically no emission in the 
region from 4 to 7ft, while beyond 9ft the spectrum is continuous, 

'Aschkinass, Ann. d. Phys., (4) 17, p. 960; 1905; Einstein, Ann. d. Phys., (4) 
17, p. 132; 1905; 22, p. 181, 569, 800; 1907. 

'Aschkinass, Verh. d. Deutsch. Phys. Ges. 17, p. loi; 1898; Rosenthal, Ann. der 
Phys., (3)«8,p. 791; 1899. 



536 Bulletin of the Bureau of Standards, \vcl #. No, /. 

and is apparently as intense as that of a complete radiator at the 
same temperature.* 

In the case of the Nernst filament, which is a combination of the 
oxides of cerium, thorium, and zirconium, the compounds of which 
are noted for their strong absorption bands, one would hardly expect 
the emission to follow the same general law of energy distribution 
known for metals. This assumption, however, has been made in the 
past, notably by Lummer and Pringsheim * and by Mendenhall and 
Ingersoll.' The first two investigators, from a rather cursory exam- 
ination of the Nernst filament, under normal power consumption, 
found a smooth continuous curve, with a maximum at wave-length 
of 1.2/i. From this and from the Wien displacement law, X,n»x = 
const, (this constant is 2940 for a black body and 2630 for platinum), 
assuming that the Nernst glower belongs to the same class of radiators 
as platinum and a black body, Lummer and Pringsheim computed 
the maximum temperature and found it to be 2450° Abs. and the 
minimum temperature 2200° Abs. Their computed energ>' curve 
of a black body having its maximum emission at i.2/i departs 
considerably from the observed curve. 

Mendenhall and IngersoU compared the emission of the Nernst 
glower in terms of a constant comparison lamp, for a certain wave- 
length in the visible spectrum, at the melting points of gold and 
of platinum. From this they extrapolated on a straight line (assum- 
ing that equation (i), known as Wien's Equation, holds for the 
glower) and found the temperature at normal or any desired power 
consumption. This leads to erroneous values, due to the fact that 
the spectrum is the composite of numerous emission bands, which 
rapidly increase in intensity, in the short wave-lengths, with rise in 
temperature. They found the normal temperature to be 2300° Abs., 
disagreeing with a recent determination by Hartman,^ who, by 
means of thermocouples of different thickness placed against the 
glower, and correcting for heat conduction by extrapolating to a 
temperature corresponding to an infinitely thin couple, found the 
temperature to be 1800° Abs. Although this method had previously 

* Rubens., Phys. Zs., 6, p. 790; 1904. 

* Lummer and Pringsheim, Verh. deut. Phys. Gesell. 8, p. 36; 1901. 
•MendenhaU and IngersoU, Phys. Rev., 24, p. 230, 1907; 25, p. i; 1907. 
^Hartman, Phy. Rev., 17, p, 65; 1903. 



Cobienu.] Selective Radiation from the Nernst Glower. 537 

been extensively used with fair success in measuring the tempera- 
ture of gas flames, it is less suited to the glower in which there is 
no layer of hot gas to even partially compensate for the heat lost 
by conduction. 

That the Nernst glower emits selectively in the visible spectrum 
has been shown by Kurlbaum and Schulze,' who found a strong 
emission band at .52/A, which became fainter with rise in tempera- 
ture and disappeared entirely at high temperatures. 

To this brief review of what has been done on the Nernst glower 
may be added a paper by its inventor,* who showed that the con- 
ductivity is electrolytic, while Kaufmann " showed that in spite of 
the entirely different inner mechanism of conduction of a gas in a 
vacuum tube and in a Nernst glower the electrodynamic phenomena 
are nevertheless very similar. 

METHODS AND RESULTS OF PRESENT INVESTIGATION. 

In the present investigation of the Nernst glower the distribution 
of radiant energy in the spectrum was determined at different energy 
consumption, and hence at different temperatures. For several 
filaments the apparent black body temperature, corresponding to 
different values of energy consumption, was measured by Drs. 
Waidner and Burgess, with an optical pyrometer, for red, green, 
and blue light. The values given in Table I were obtained from 
their watt-temperature curve, ^extrapolated for high temperatures. 
These values are of interest in showing the variation in selective 
emission with rise in temperature. 

The apparatus used in this work consisted of a spectrometer," 
having mirrors 10 cm in diameter and of 50-cm focal length, a 
perfectly clear fluorite prism, having an angle of 60° and circular 
faces 33 mm in diameter, and a bolometer " with a hemispherical 
reflecting mirror. The bolometer strip and spectrometer slit were 
0.6 mm. wide, or about 4' of arc. The upper part of the spec- 

" Kurlbaum and Schulze, Verh. d. Deutsch. Phys. GeseU, o, p. 428; 1903. 
• Nernst Zs. fiir. Electrochemie, 6, p. 41; 1899. 
*• Kaufmann, Ann. d. Phys., (4) 2, 158 p.. 1900; 6, p. 757; 1901. , 
**For adjustments see '* Investigations of Infra-red Spectra," Vol. i; Carnegie 
Inatitute of Washington, 1905. 
^' Described in this Bulletin, 4, p. 391. 



538 Bulletin of the Bureau of Standards. [Voi.4.no,4. 

trometer, containing the coUimating mirrors, and the Wadsworth 
mirror-prism table were entirely inclosed by a thin sheet-metal 
box, lined with black velvet. The spectrometer slit was covered 
with a clear plate of fluorite. The openings in the top for adjusting 
the mirrors were closed with soft wax, while the hole admitting the 
axis for rotating the mirror-prism table was tightened with a nut 
and packing. 

Within the box, and below the level of the mirrors, were placed 
vessels containing phosphorous pentoxide and sticks of potassium 
hydroxide, which entirely eliminated the absorption bands of CO, 
and water vapor from the emission curves. A water-cooled shutter 
was placed before the spectrometer slit and the Nemst glower, 
inclosed in an asbestos case to prevent air currents, was placed close 
to the shutter. Observations were also made without inclosing the 
glower, to prove that the effects observed are not due to stray radia- 
tion from the asbestos case. 

The auxiliary galvanometer'** of 5.3 ohms resistance, with a 
single swing of 4 to 5 seconds, had a current sensibility of fc = 1.6 to 1.5 
X 10"" ampere. A greater sensitiveness for the same period would 
have been possible, by using a lighter suspension. The present 
suspension of 10 magnets was just heavy enough so as not to be 
aflFected by tremors. By reducing the number of magnets from 12 
to ID and by placing the mirror at the center of the suspension the 
sensibility was increased by 100 per cent. Using a bolometer current 
of .04 ampere the computed temperature sensibility was 5° x io"*C., 
which was generally far in excess of that required. The deflections 
were reduced to 14 to 15 cm by inserting resistance in series with 
the galvanometer. The individual readings varied by i mm, or 
less than i per cent, which is as close as the nature of the work 
required, since the actual deflections were as high as 2000 cm. 
Furthermore, at high temperatures (especially when run above 
normal power consumption) the filament changed in emission by 
that amount during the series of observations. 

1'* Described in this Bulletin , 4, p. 432. The coils of this instrument are 32 mm 
in diameter. The proportionality of the deflections with current, at this sensibility, 
was exact up to 18 cm. 



Cobienu.] SelccHve Radiation from the Nernst Glower. 539 

The calibration curve of the fluorite prism was constructed from 
the refractive indices, found by Paschen," which, after plotting all 
the observations made by different observers, seems to be as close to 
the most probable values as observation will permit. Unfortunately 
the dispersion curve passes through a double curvature at 1.5/Di, just 
where the energy spectra have their maxima. In this region the 
correction for purity (the so-called "slit- width'* correction) is a 
maximum. 

The wave-lengths in the calibration curve were plotted to the 
fourth decimal place, so that there is a certainty of the values to at 
least the second decimal place. This, however, is of less importance 
than the value of the slit-width correction, which was made accord- 
ing to Paschen," the values being obtained from a curve plotted 
on a large scale to insure an accuracy greater than required in the 
work. In a few cases a correction was made for the reflecting 
power of the silver mirrors, but it was found negligible except in 
the visible spectrum. 

With this apparatus a series of energy curves was obtained, vary- 
ing the energy consumption from 16 watts (the lowest at which the 
glower would conduct without using a transformer) to 123 watts, 
which is far above the normal. The energy curves, which were 
continuous, underwent great variations in appearance with rise in 
temperature. At 2.5 and 3.5ft elevations and depressions would 
generally appear in the curves, which could not be attributed to 
experimental errors. Since previous work seemed to show that the 
spectrum is continuous, an attempt was made to locate the cause of 
the disagreement in the apparatus, the calibration, or in the slit- 
width correction curve, but without avail until the filament was 
run on a 2000-volt transformer which permitted a low heating of 
the glower. At the lowest temperature the glower was a grayish 
red. The results given in Fig. i are for a no- volt A. C. glower 
No. 118, each point being the mean of at least two observations. 
The ordinates are about three times the observed galvanometer 
deflections. These results are entirely different from anything 
hitherto observed in the emission of solids in the infra-red. At the 

'•Paschen, Ann. d. Phys., (4) 4, p. 299; 1901. 
"Paschen, Ann. d. Phys., (3) 60, p. 714; 1897. 



540 



Bulletin of the Bureau of Standards. 



[Voi. 4, i^o, 4. 



































cm 

180 








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160 








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r« 



Rg. 2.-'Nemst Glower, No, 118. 
a s= 17 watts, d = 21.8 watts, c = ** black body." 



Cobieniz.] SclecHve Radiation front the Nernst Glower. 541 

lowest temperatures (8cx>-900° C.) the bands in the region of long 
wave-lengths are the most intense. As the temperature increases, 
the bands in the region of 2.5^1 increase very rapidly in intensity, so 
that by the time the temperature has increased to icxx)° to 1100°, 
the intensity of the group of bands at 2fi is far in excess of that 
at 5.5A*. 

The depression at 3 to 3.5^1 persists even at normal energy con- 
sumption. The curves at higher temperatures often show a slight 
depression at 2.5^1 not attributable to experimental errors. As the 
temperature rises (curve ^, Fig. i) new emission bands appear, nota- 
bly at 2.5fi and at 4^1. This shift of the maximum intensity of the 
bands, with increase in temperature, is to be expected, if the emis- 
sion is a purely thermal one, following KirchhofPs law, and is the 
most conspicuous illustration yet recorded. 

In Fig. 2 the emission curves are shown for a iio-volt glower 
(serial number 118) at 17 and 21.8 watts respectively. It should be 
noticed that the emission curve has become smooth and continuous, 
with but two maxima, at 1.4 and 5.5/* respectively. The curve c 
for a black body, having a temperature corresponding to maximum 
at 1.65^1 and of the same intensity as that of the filament at this 
point, falls far below the emission curve at 5.5^1. This shows that 
the maximum at 1.65/x is not as high as it should be, if the glower 
followed a radiation law similar to that of a complete radiator or 
platinum, as was heretofore assumed. 

In Fig. 3 is shown a series of energy curves of a 200-volt filament, 
at different power consumptions, viz: a = 15.8, b = 17.6, c = 19.2, 
d = 22.1, e = 27.1, /= 34.6, g = 43.3, h = 52.7, k = 62.4 watts 
respectively. This illustrates very well the elimination of the emis- 
sion minimum at 4^1. The curves are for the same sensibility", 
80, of the galvanometer as compared with the sensibility of 105 in 
Fig. I. 

The radiation of a iiovolt filament. No. 118, at a power con- 
sumption of 77.7 watts is given in Fig. 4, curve a. In the same 
figure, curve b represents the distribution of energy of a 220-volt 
filament (No. 120) at a power consumption of 102.5 watts, which is 

" For convenience, in practice the sensibility is expressed in arbitrary units which 
will be described elsewhere. 



ctn 




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44 




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^ 


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[% 


i 


12 




V. 


— ^ 


^ 

^ 

y 


'A 






^->. 


8 






.^ 




Fig. 3. RADIATION FROM A aoo-VOLT GLOWER. 

a =15.8, * = i7.6,f= 19.2, rf=aa.i.^ = 27.1,/= 34.6, 

g = 44.3, k = 52.7, i = 624 w«tt». 


4 


















3 


e 4 


i 


. 




\ • 


• ( 


5 •• 



542 



Cobienu.] Selective Radiation from the Nernst Glower. 



543 



somewhat above the normal. The energy distribution is irregular, 
with an abnormal increase in intensity at 0.75^1 due no doubt to the 
sudden increase in intensity of an emission band, as illustrated in 




Fig. I. Fig. 5 shows the radiation curve of the 220-volt filament 
(No. 120) at 123 watts, which is far above the normal. The emis- 
sivity decreased rapidly in intensity, probably due to the evapora- 
22832 — 08 — 6 



544 



Bulletin of the Bureau of Standards. 



[yo/.4. !^o.4. 



tion and decrease in diameter of the filament. Within the experi- 
mental errors of observation the results indicate that the emissivity 
is abnormally increased in the visible. The theoretical curve of a 
"black body," having a maximum emission coinciding with that of 
the glower at 1.3^1 {t = 1975° C.) falls below the obser\^ed curv^e in 
the visible, and is higher than the observed curve at 5/1, which is 











■V 






































cm 






/ 


\ 












































/ 




^ 






Fig. 5 

RADIATION FROM NERNST GLOWER ON 1 23 WATTS 

200 VOLTS (No.120).SENSIBiLITY«91 

Curve b Mcomptrtod curve for black body whan its 

maximum is«t 1.307» 










1 




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I 




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1800 












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1 












































uS 1200 




1 
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600 




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just the reverse of the results obtained when using 16.8 watts. (See 
Fig. 2 for a similar case.) Since the galvanometer deflections were 
as high as 2cxx) cm and since errors as great as 25 to 30 per cent 
would be necessary to account for this discrepancy, it is evident that 
the radiation from the glower can not be compared with that of a 
complete radiator. The data obtained at low temperatures (Fig. i), 
which indicate selective emission, are a further proof of this con- 
clusion. An attempt was made to find the transmission of a thin 



Codiemiz] SclecHve Radiation from the Nemst Glower. 



545 



section made of the material which constitutes the glower, but with- 
out success, due to the inhomogeneity of the material. As a substi- 
tute, the radiation from (and through) a 0.5 mm layer of this 

























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3 4 5 6 7M 

Fig. 6. Radiation /rom Nemst {A, C). Material, 
Curves a and b. Curve c = radiation from a Nemst heater tube. 

material was found when placed on a strip of platinum heated elec- 
trically, or placed on a "heater tube " of a Nemst lamp from which 
the covering of kaolin had been removed. The surface was a deep 



546 Bulletin of the Bureau of Standards, [roi. 4. J^'o. 4. 

red, temperature about gcx)® C, similar to the filament in Fig. i. 
The platinum was probably at a temperature of 1200? In Fig. 6 
is given the emission curves, a and d,.of the glower material on the 
"heater tube." The emission bands at 2, 2.7, and 6/1 are similar to 
those found in Fig. i, but there is no great depression at 4/i, from 
which it would appear that this region is filled up by the radiation 
from the platinum wires, transmitted through the glower material. 
This is to be expected from the conditions indicated in Fig. i. 
Curve Cy Fig. 6, shows the radiation from a Nernst *' heater tube," 
the covering being a refractory clay. An examination of the mate- 
rial separately will be necessary to show whether or not the maxima 
are true emission bands. The importance of such a radiator is evi- 
dent in investigations in which a more uniform distribution of 
energy is desired than obtains in the glower, e. g. in searching for 
reflection bands of substances. 

The radiation '^constant," a, was found for several glowers, using 
equation (2). In order to do this it is necessary to accurately find 
the wave-length {\^j,) corresponding to the point of maximum emis- 
sion. This is possible from equation (i) by selecting two wave- 
lengths, \ and Xj, corresponding to the points where the value of E^ 
the galvanometer deflections, is the same. This gives: 

In Table I are given the mean values of \^^ determined from 
several points on each cur\'e. The maximum and minimum tem- 
peratures computed on the assumption that the glower follows a 
radiation law similar to that of a complete radiator and that of plati- 
num, respectively (which of course is not true), are also given in this 
table. The apparent temperatures, determined with the optical 
pyrometer are included, to indicate changes in selectivity'' with rise 
in temperature. The values of a are plotted in Fig. 7, the wave- 
lengths being selected to correspond with those used in finding \^^ 
(eq. 3) in order to facilitate computation. For the 200-volt filament 
the so-called constant, a, drops from 7.5 at an energy consumption of 
16 watts to a unifonn value of 5.3 at 80 to 120 watts.'* For the 

"Excepting the curve for 102 watts, which is very irregular, showing unresolved 
bands of selective emission. 



coUtnu.] Selective Radiation from the Nernst Glower. 



547 




iO ' ^40 TeO ' 60 ■ 100 

Fig. 7. Radiation constant, a, of Nernst Glower, 



T20^ATP 




WATTiio 20 30 40 50 60 70 80 90 100 110 120 ,»cai£ or watts 

(NERMT OLOWER) 
•CAtl or TEMPERATURES CPLATIHUM AND aiACKBOOV) 1000* 1200* 1400* 1600* 1800* 2000* 2200" 2400* A»S. 



548 



Bulletin of the Bureau of Standards. 



\^Vol.4.^'o.4. 



TABLE I. 



Watts 
amp. 



Temp. 
K. red 



Temp. 
K. ffreen 



Temp. 
K. blue 



Neinst 200 VoltSy No. 120. 



Nemst 220 Volta. 



T —^930 

— «73° 



a6ao 



-nt 



16.8 watts 


1400*»C 












0.11 amp. 


9452*» 


1490 


1517 


1.458m 


1737 


Wn** 


19.6 watts 


1460 






(1.433) 






0.12 amp. 


1490 


1527 


1550 


1.45m 


1747 


1532 


27.7 watts 


1602 












.167 amp. 


1627 


1659 


1677 


1.445m 


1757 


1544 


83.2 watts 


1985 












.412 amp. 


2027 


2052 


2064 


1.366m 


1877 


1647 


102.5 watts 


2055 




• 


1.317 


1950 


1715 


0.5 amp. 


2120 


2148 


2158 








123. watts 








1.307m 


1972 


1735 


.6 amp. 


















Nemst 110 Volts, N< 


>. 118. 






17. watts 


1400° C 






1.621m 






.2 amp. 


1438 


1470 


1484 




1537 


1342 


77.7 watts 


2110 






1.388 






.80 amp. 


2135 


2170 


2988 




1842 


1612 






NemstllOD. C, N< 


». 121. 






18.4 watts 


1468 


1507 


1528 


1.560 


1607 


1406'* 


.2 amp. 


1465 













f 19.6 watts 








1.583 


1577 


1382 


.115 amp. 














37.2 watts 








1.448m 


1747 


1537 


.20 amp. 














f 83. watts 








1.360m 


1879 


1652 


t .4 amp. 















56 

54 
52 
50 
48 
46 
44 
42 
40 
36 
36 
34 
32 
^30 




































/ 


> 
































\ 






Fig. 9 
RADIATION FROM A NCRNST GLOWER (110 VOLT) 
Oa 7.6 watts 
5« 9.5 watte 
C « 1 2 watts(not to *am« tcala at a and &) 










\ 












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24 
22 
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12 
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549 



550 Bulletin of the Bureau of Standards. \voi. 4. No. 4^ 

22ovolt glower (No. 120) the value of a decreases from 6.3 to 5.3, 
while for a iiovolt D. C. glower the value changes from 6.9 to 5.30, 
In other words, the total emissivity drops from the 6th power to 
the 4.3th power of the absolute temperature. By taking the total 
radiation of the glower, Mendenhall and IngersoU foimd the value 
of a to be about 9, with no consistent evidence of a variation 
of a with temperature. These results were obtained before the 
emission spectrum w^as resolved into separate bands. Fig. i. From 
the latter it is evident that it is not permissible to apply this method 
of determining the ** constant." In Fig. 8 is given a comparison of 
the ratio of the intensities of the emissivities of various glowers at 
various values of energy consumption for wave-lengths of 5.5^1 (the 
position of the apparently second maximum, Fig. 2) and of X„^, 
which, of course, varies with temperature. The thicknesses of the 
filaments were: ^ = .63 mm, b = .yi mm, ^=.98 mm, ^=1.05 mm, 
respectively. The ratio rises from a value of 5 at 18 watts to a 
fairly constant value of about 25 at normal power consumption, i. e., 
the point on the potential-current curve where the potential is fairly 
constant. This ratio is a function of the thickness, and is an exact 
analog of what is found in the discharge of electricity through gases. 
In this figure this same ratio is plotted for a complete radiator and 
for platinum at various temperatures, from which it will be observed 
that the ratio is far from approaching an asymptotic value. 

From whatever point of view we consider the data at hand, it is 
evident that even after the emission spectrum has become apparently 
continuous it does not follow so simple a law as has been established 
for solids emitting continuous spectra. It is also evident that any 
estimations of the temperature of the glower, based on these laws, 
will lead to erroneous results. From a commercial point of view, 
the efficiency of such a radiator, in which the emissivity is abnormally 
high at .6 to .7ft, while the maximum at 1.2/1 is abnormally low, 
must be much higher than that of substances having a radiation 
law similar to that of platinum, in which case, in order to attain a 
similar intensity in the visible spectrum, the maximum at i.2fi rises 
to extremely high values. 



codimtz] Selective Radiation from the Nernst Glower, 551 

By integrating the energy curve and taking the ratio of the visi- 
ble to the infra-red radiation (it has been customary to take the 
dividing line at .76^1) it is possible to obtain a rough estimate of the 
luminous (white light) eflficiency for a given energy consumption. 
This gives values from 3.6 per cent at 27.7 watts, 5.5 per cent at 83 
watts to 7.4 per cent at 123 watts. The total areas can not be com- 
pared, particularly for different filaments, because the cone of energy 
which enters the spectrometer slit does not cover more than about 
one-half of the prism face, and varies with the diameter of the fila- 
ment and its distance from the slit. This will change the size of 
the galvanometer deflections uniformly throughout the spectrum. 
Thus in Fig. 4 the areas of the curves can not be compared, 
because they are for different filaments; but curve b might be com- 
pared with Fig. 5. This is of minor importance, for the curves are 
given to show the change in the relative distribution of energy with 
rise in temperature. 

The results described in this paper are for filaments made from 
different lots of material, the 220-volt glower being at least 5 years 
old. The observations have been made at different dates, all in 
duplicate, some quadruplicate. 

An examination of other filaments may show a variation in the 
minor details of the two groups of emission bands, as shown in Fig. 
9, but the general results can hardly be modified without employing 
a much larger dispersion and a narrower bolometer. This, how- 
ever, is of minor importance in considering the selective emission of 
the Nernst glower. The manner in which some of these emission 
bands are suppressed while others are intensified in different sub- 
stances will be described in a subsequent paper. 

Washington, February 10, 1908. 



**-»- .■^' 



THE TESTING OF GLASS VOLUMETRIC APPARATUS. 



By N. S. Osborne and B. H. Veazey. 



CONTENTS. 

I. Introduction 554 

II. Spbcipications for Gi^ass Voi«umetric Apparatus: 

1. Types of apparatus admitted for test 556 

2. General specifications — 

{a) Units of cstpacity employed 556 

[d) Standard temperature 556 

(c) Material and annealing 556 

{d) Design and workmanship 556 

{e) Inscriptions 557 

3. Special requirements— 

{a) Flasks 557 

(b) Cylinders 559 

{c) Transfer pipettes 559 

{d) Burettes and measuring pipettes 560 

{e) Burette and pipette tips 560 

4. Special rules for manipulation — 

(fl) Test liquid 560 

(b) Method of testing 561 

(r) Cleanliness of apparatus 561 

(d) Flasks and cylinders 561 

(e) Pipettes and burettes 562 

5. Tolerances — 

(a) Flasks 562 

{b) Transfer pipettes 562 

{c) Burettes and measuring pipettes 563 

{d) Cylinders 563 

(e) Delivery time 563 

III. Tests mads by the Bureau of Standards: 

1. Nature of tests 564 

2. Precision stamp 564 

3. Certificates of capacity 564 

4. Special tests 564 

553 



554 Bulletin of the Bureau of Standards. \voi. 4, No, 4. 

IV. Discussion of Generai. Specifications: page. 

1 . Units of capacity 565 

2. Standard temperature 565 

3. Material and annealing 566 

4. Inscriptions 566 

V. Manipui^ation: 

1. Method of reading 566 

2. Cleanliness of apparatus 567 

3. Use of liquids other than water 574 

4. Effect of temperature on residue in burettes and pipettes 578 

5. Avoidance of unnecessary heating of apparatus 579 

VI. Fi^ASKS AND Cylinders: 

1. Difference in volume delivered and contained 579 

2. Use of special liquids 580 

VII. Transfer Pipettes: 

I. Design 581 

VIII. Burettes and Measuring Pipettes: 

1 . Burette drainage and outflow time 583 

2. Use of special liquids 585 

3. Calibration 5S6 

4. Measuring pipettes 587 

5. Lrimits of error 587 

IX. Methods of Testing: 

1 . Preliminary examination 58S 

2. Methods of cleaning apparatus 588 

3. Measurement of capacity' — 

(a) Testing flasks by direct measurement 588 

{b) Testing flasks, pipettes, and burettes by weighing 590 

(r) Calculation of capacity 592 

{d) Tables used in calculating capacity 594 



INTRODUCTION. 

The Bureau of Standards published November i, 1904, Bureau 
Circular No. 9, on "Testing of glass volumetric apparatus," contain- 
ing specifications for glass volumetric apparatus, the verification of 
which would be undertaken, and also regulations for testing such 
apparatus. 

As stated in the circular, the specifications with few exceptions 
were made to agree with those recommended by a committee of the 
American Chemical Society, consisting of Prof. E. W. Morley, chair- 
man; Prof. Arthur A. Noyes; Prof. Theodore W. Richards, and Mr. 
E. E. Ewell. 



K«i"' ] Testing of Glass Volumetric Apparatus, 555 

In preparing the specifications, the regulations of the Kaiserliche 
Normal-Eichungs-Komniission of Germany were freely drawn upon 
and in many cases adopted without appreciable change. In cases, 
however, where the experimental work of this bureau indicated the 
desirability of modifications they were adopted. 

Since the first publication of these regulations slight changes, sug- 
gested by the work of testing, have been introduced by revision of 
Circular No. 9, as "second edition," January 16, 1905, and "third 
edition," February i, 1906. 

From the fact that some diflficulty has been experienced by manu- 
facturers in complying with the specifications, and that users of 
apparatus have written in certain cases for explanations of the regu- 
lations, and also since several additional changes are deemed advis- 
able, the occasion of the third revision of the regulations is taken to 
discuss in more detail the various specifications and rules for manip- 
ulation, to publish the results of experimental work having a direct 
bearing on construction and use, and to describe the methods em- 
ployed at this bureau in testing volumetric apparatus. 

A number of tables compiled for use in this work have been added 
for the convenience of those wishing to do their own testing. 

The regulations included in this article, consisting of general speci- 
fications, special requirements, rules for manipulation, limits of error, 
and tests performed by this bureau, are as last revised and in the 
form shortly to be issued in Bureau Circular No. 9, fourth edition. 

n. SPECIFICATIONS FOR GLASS VOLUMETRIC APPARATUS ACCEPTED 

FOR TEST. 

The primary purpose of these specifications is to define the requi- 
site qualifications for precision apparatus. 

The bureau aims to encourage excellence in quality by coopera- 
ting with makers and users of apparatus, and to this end endeavors 
to assist manufacturers in establishing standards and perfecting 
methods. In order that users of standardized apparatus may fully 
benefit by the facilities of the bureau it is necessary for them when 
purchasing apparatus to be submitted for test to require that the 
apparatus shall comply with the specifications. By admitting for 
test only apparatus conforming to these standards the work of test- 



556 Bulletin of the Bureau of Standards, \voi. 4.^0. a. 

ing is confined to apparatus whose utility is sufficient to justify the 
labor expended in the accurate calibration. Certain of the specifi- 
cations, such as those regarding quality of glass and process of an- 
nealing before calibration, are for their fulfillment dependent largely 
on the integrity of the maker. Only by supporting conscientious 
makers in giving consideration, first, to quality, and, second, to 
cost, can users of standardized apparatus secure a high degree of 
excellence. 

1. Types of Apparatus which will be Regularly Admitted for 
Test. — Measuring flasks ; measuring cylinders, with or without sub- 
divisions; transfer pipettes, i. e., without subdivisions; burettes and 
measuring pipettes, with partial or complete subdivisions. 

2. General Specifications — 

{a) Units of capacity. — The liter, defined as the volume occupied 
by a quantity of pure water at 4° C. having a mass of 1 kilogram, 
and the one-thousandth part of the liter, called the milliliter or cubic 
centimeter,* are employed as units of capacity. 

{b) Standard temperature. — Twenty degrees Centigrade is regarded 
by the bureau as the standard temperature for glass volumetric appa- 
ratus, and an extra charge will be made for testing apparatus gradu- 
ated for use at other temperatures. 

(c) Material and annealing. — The material should be of best 
quality of glass, transparent and free from striae, which adequately 
resists chemical action, and has small thermal hysteresis. All appa- 
ratus should be thoroughly annealed at 400° C. for 24 hours and 
allowed to cool slowly before being graduated. 

(d) Design and workmanship. — The cross section must be circular 
and the shape must permit of complete emptying and drainage. 

Instruments having a base or foot must stand solidly on a level 
surface, and the base must be of such size that the instruments will 
stand on a plane inclined at 15°. Stoppers and stopcocks must be 
so ground as to work easily and prevent leakage. 

The parts on which graduations are placed must be cylindrical 
for at least i cm on each side of every mark, but elsewhere may be 
enlarged to secure the desired capacities in convenient lengths. 

* The cubic centimeter is not exactly the one-thousandth part of the liter, but the 
difference is of no consequence in volumetric analysis. 



Veazey. J 



Testing of Glass Voluntettic Apparatus. 



557 



The graduations should be of uniform width, continuous and finely 
but distinctly etched, and must be perpendicular to the axis of the 
apparatus. All graduations must extend at least halfway around, 
and on subdivided apparatus every tenth mark, and on undivided 
apparatus all marks must extend completely around the circum- 
ference. 

The space between two adjacent marks must not be less than i 
millimeter. The spacing of marks on completely subdivided appa- 
ratus must show no evident irregularities, and sufficient divisions 
must be numbered to readily indicate the intended capacity of any 
interval. Apparatus which is manifestly fragile or otherwise defect- 
ive in construction will not be accepted. 

{e) Inscriptions, — Every instrument must bear in permanent leg- 
ible characters the capacity in liters or cubic centimeters, the tem- 
perature in Centigrade degrees at which it is to be used, the method 
of use, i. e., whether to contain or to deliver, and on instruments 
which deliver through an outflow nozzle the time required to empty 
the total nominal capacity with unrestricted outflow must be like- 
wise indicated. 

Every instrument should bear the name or trade-mark of the 
maker. Every instrument must bear a permanent identification 
number, and detachable parts, such as stoppers, stopcocks, etc., 
belonging thereto must bear the same number. 

Figs. I, 2, and 3 (two-fifths natural size) illustrate several arrange- 
ments of designating marks which are considered suitable. 

3. Special Requirements. — {a) Flasks, — At the capacity mark or 
marks on a flask the inside diameter should be within the following 
limits: 



Capacity of flask (in cg) up to and 
including 

MaxJiniiTn diameter (in mm) 

Minimwin diameter (in mm) 



2,000. 


1,000 


500 


250 


200 


100 


50 


25 


20 


18 


15 


13 


12 


10 


18 


14 


12 


10 


9 


8 


6 



25 

8 
6 



The neck of a flask must not be contracted above the graduation 
mark. 



558 



Bulletin of the Bureau of Standards. [p^ol 4, No. 4. 




Fig. 1. 




N0.215 

DELIVERS 

100 CC 

20<»C 

ao SEC. 



Fig. 2. 




i 




Fig. 3. 



Osbom£.'^ 
Veazey. J 



Testing of Glass Volumetric Apparatus, 



559 



The capacity mark on any flask must not be nearer the end of the 
cylindrical portion of the neck than specified below: 



Capacity 


Distance from Upper 
End 


Distance from Lower 
End 


100 cc or less 


3 cm 
6 " 


1 cm 


More than 100 cc. . . . .... 


2 " 







Flasks of I liter or more but not less may be graduated both to 
contain and to deliver, provided the intention of the different marks 
is clearly indicated. 

(U) Cylinders. — Only cylinders graduated to contain will be 
accepted for test. 

The inside diameter of cylinders must not be more than one-fifth 
the graduated length. 

{c) Transfer pipettes. — Pipettes for delivering a single volume 
are designated " transfer " pipettes. 

The suction tube of each transfer pipette must be at least i6 cm 
long, and the delivery tube must not be less than 3 cm nor more 
than 25 cm long. 

The inside diameter of any transfer pipette at the capacity mark 
must not be less than 2 mm and must not exceed the following 
limits: 



Capacity of pipettes (in cc) op to and including . 
Diameter (in mm) 



25 

4 



50 
5 



200 
6 



The outside diameter of the suction and delivery-tubes of transfer 
pipettes exclusive of the tip must not be less than 5 mm. 

The capacity mark on transfer pipettes must not be more than 6 
cm from the bulb. 

The outlet of any transfer pipette must be of such size that the 
free outflow shall last not more than one minute and not less than 
the following for the respective sizes: 



Capacity (in cc) op to and including. 
Outflow time (in seconds) 



5 

15 



10 
20 



50 
30 



100 
40 



200 
50 



22832—08 7 



560 



Bulletin of the Bureau of Standards. 



\yol.4.No,4, 



(d) Burettes and measuring pipettes, — Only those emptying 
through a nozzle permanently attached at the bottom are accepted 
for test. 

The distance between the extreme graduations must not exceed 
65 cm on burettes nor 35 cm on measuring pipettes. 

The rate of outflow of burettes and measuring pipettes must be 
restricted by the size of the tip and for any graduated interval the 
time of free outflow must not be more than three minutes nor less 
than the following for the respective lengths: 



Length Graduated 


Time of Outflow 


Length Graduated 


Time of Outflow 


65 Centimeters 


140 Seconds 


35 Centimeters 


60 Seconds 


60 " 


120 " 


30 " 


50 " 


55 " 


105 " 


25 " 


40 " 


50 " 


90 " 


20 " 


35 " 


45 " 


80 " 


15 " 


30 " 


40 " 


70 " 







The upper end of any measuring pipette must be not less than 
10 cm from the uppermost mark and the lower end not less than 4 
cm from the lowest mark. 

{e) Burette and pipette tips. — Burette and pipette tips should be 
made with a gradual taper of from 2 cm to 3 cm, the taper at the 
extreme end being slight. 

A sudden contraction at the orifice is not permitted and the tip 
must be well finished. 

In order to facilitate the removal of drops and to avoid splashing 
when the instrument is vertical, the tip should be bent slightly. 

The approved form of tips for burettes, measuring pipettes, and 
transfer pipettes is shown in fig. 4. 

4. Special Rules for Manipulation. — ^These rules indicate the 
essential points in the manipulation of volumetric apparatus which 
must be observed in order that the conditions necessary to obtain 
accurate measurements may be reproduced. 

[a) Test liquid. — Apparatus will be tested with water and tlie 
capacity determined will, therefore, be the volume of water con- 
tained or delivered by an instrument at its standard temperature. 



Veazey. J 



Testing of Glass Volumetric Apparatus, 



561 



{b) Method of reading, — In all apparatus where the volume is 
limited by a meniscus the reading or setting is made on the lowest 
point of the meniscus. In order that the lowest point may be 
observed it is necessary to place a shade of some dark material 
immediately below the meniscus, which renders the profile of the 
meniscus dark and clearly visible against a light background. A 
convenient device for this purpose is a collar-shaped section of thick 
black rubber tubing, cut open at one side and of such size as to clasp 
the tube firmly. 

{c) Cleanliness of apparatus, — Apparatus must be sufiSciently 
clean to permit uniform wetting of the surface. 



^ 



f 




Fig. 4 (two-fifths natural size). 



{d) Flasks and cylinders, — In filling flasks and cylinders the entire 
interior of the vessel will be wetted, but allowed a sufficient time to 
drain before reading. Before completely filling to the capacity mark 
flasks should be well shaken to completely mix the contents. 

Flasks and cylinders when used to deliver should be emptied by 
gradually inclining them until when the continuous stream has 
ceased they are nearly vertical. After half a minute in this position 
the mouth is brought in contact with the wet surface of the receiving 
vessel to remove the adhering drop. 



562 



Bulletin of the Bureau of Standards, 



[ Vol. 4. No. 4. 



(e) Pipettes and burettes, — In filling pipettes and burettes excess 
liquid adhering to the tip should be removed when completing the 
filling. 

In emptying pipettes and burettes they should be held in a vertical 
position, and after the continuous unrestricted outflow ceases the tip 
should be touched with the wet surface of the receiving vessel to 
complete the emptying. 

Stopcocks, when used, should be completely open during emptying. 

Burettes should be filled nearly to the top, and the setting to the 
zero mark made by slowly emptying. 

While under normal usage the measurements ordinarily are from 
the zero mark, other initial points may be used on burettes of 
standard form without serious error. 

5. Tolerances. 

(a) Flasks. 



Capacity Less Than and 
including 




Limit of Error 




If to Contain 




If to Deliver 


25 CG 


0.03 CC 






0.05 CC 


50 " 


.05" 






.10" 


100 " 


.08" 






.15" 


200 " 


.10" 






.20" 


300 " 


.12" 






.25" 


500 " 


.15" 






.30" 


1,000 " 


.30" 






.50" 


2,000 " 


.50" 






1.00" 



(b) Transfer pipettes. 



1 Than and Including 


Limit of Error 




2CC 


0.006 CC 




5" 


.01 






10" 


.02 






30" 


.03 






50" 


.05 






100" 


.08 






200" 


.12 


u 





Veazey, J 


Testing of Glass Volumetric Apparatus. 563 




(c) Burettes and measuring pipettes. 


Capacity 
Portion 
eluding 


of Total Graduated 
Less Than and In- 


Limit of Error of Total or Partial Capacity 


Burettes 


Measuring Pipettes 




2CC 
5" 




0.01 CC 




0.01 CC 


.02" 




10" 


.02" 


.03" 




30" 


.03" 


.05" 




50" 


.05" 


.08" 




100" 


.10" 


.15" 



Further, the error of the indicated capacity of any ten consecu- 
tive subdivisions must not exceed one-fourth the capacity of the 
smallest subdivision. 

(d) Cylinders. 



Capacity of Total Qrad- , ,^j^ ^^ i?,,«, ^t t^^-i When the Smallest Sub- 
uate/ Portion Less , "^'^nfa, glpl^ty divisions are Not 



Than and Including 



30 CC 

50 " 

100 " 

200 " 

500 " 

1,000 " 

2,000 " 



0.06 CC 

.10 " 

.30 " 

.50" 

1.20 " 

2.00 " 

4.00 " 



More Than 

0.2 CC 

1.0" 

2.0 " 

10.0 " 

20.0 " 



Limit of Error of any 

Ten Consecutive 

Divisions 



0.1 CC 

.2 " 

.4 " 

1.0 " 

2.0 " 



The delivery time marked on any instrument must be within the 
limits prescr